2 %%Creator: dvips(k) 5.96.1 Copyright 2007 Radical Eye Software
4 %%CreationDate: Tue May 26 11:12:48 2009
7 %%BoundingBox: 0 0 596 842
8 %%DocumentFonts: Times-Roman Times-Bold LMRoman12-Regular CMSY10 CMMI12
9 %%+ CMR8 Times-Italic CMR12 CMMI8 dsrom12 Courier
10 %%DocumentPaperSizes: a4
12 %DVIPSWebPage: (www.radicaleye.com)
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15 %DVIPSSource: TeX output 2009.05.26:1112
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62 %%BeginProcSet: 8r.enc 0 0
63 % File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30
66 % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry,
67 % W. Schmidt, P. Lehman",
70 % filename = "8r.enc",
71 % email = "tex-fonts@@tug.org",
72 % docstring = "This is the encoding vector for Type1 and TrueType
73 % fonts to be used with TeX. This file is part of the
74 % PSNFSS bundle, version 9"
77 % The idea is to have all the characters normally included in Type 1 fonts
78 % available for typesetting. This is effectively the characters in Adobe
79 % Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol,
80 % MacRoman, and some extra characters from Lucida.
82 % Character code assignments were made as follows:
84 % (1) the Windows ANSI characters are almost all in their Windows ANSI
85 % positions, because some Windows users cannot easily reencode the
86 % fonts, and it makes no difference on other systems. The only Windows
87 % ANSI characters not available are those that make no sense for
88 % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
89 % (173). quotesingle and grave are moved just because it's such an
90 % irritation not having them in TeX positions.
92 % (2) Remaining characters are assigned arbitrarily to the lower part
93 % of the range, avoiding 0, 10 and 13 in case we meet dumb software.
95 % (3) Y&Y Lucida Bright includes some extra text characters; in the
96 % hopes that other PostScript fonts, perhaps created for public
97 % consumption, will include them, they are included starting at 0x12.
98 % These are /dotlessj /ff /ffi /ffl.
100 % (4) hyphen appears twice for compatibility with both ASCII and Windows.
102 % (5) /Euro was assigned to 128, as in Windows ANSI
104 % (6) Missing characters from MacRoman encoding incorporated as follows:
106 % PostScript MacRoman TeXBase1
107 % -------------- -------------- --------------
110 % /lessequal 178 0x18
111 % /greaterequal 179 0x19
112 % /partialdiff 182 0x1A
113 % /summation 183 0x1B
119 % /approxequal 197 0x8F
125 /.notdef /dotaccent /fi /fl
126 /fraction /hungarumlaut /Lslash /lslash
127 /ogonek /ring /.notdef /breve
128 /minus /.notdef /Zcaron /zcaron
130 /caron /dotlessi /dotlessj /ff
131 /ffi /ffl /notequal /infinity
132 /lessequal /greaterequal /partialdiff /summation
133 /product /pi /grave /quotesingle
135 /space /exclam /quotedbl /numbersign
136 /dollar /percent /ampersand /quoteright
137 /parenleft /parenright /asterisk /plus
138 /comma /hyphen /period /slash
140 /zero /one /two /three
141 /four /five /six /seven
142 /eight /nine /colon /semicolon
143 /less /equal /greater /question
152 /X /Y /Z /bracketleft
153 /backslash /bracketright /asciicircum /underscore
163 /bar /braceright /asciitilde /.notdef
165 /Euro /integral /quotesinglbase /florin
166 /quotedblbase /ellipsis /dagger /daggerdbl
167 /circumflex /perthousand /Scaron /guilsinglleft
168 /OE /Omega /radical /approxequal
170 /.notdef /.notdef /.notdef /quotedblleft
171 /quotedblright /bullet /endash /emdash
172 /tilde /trademark /scaron /guilsinglright
173 /oe /Delta /lozenge /Ydieresis
175 /.notdef /exclamdown /cent /sterling
176 /currency /yen /brokenbar /section
177 /dieresis /copyright /ordfeminine /guillemotleft
178 /logicalnot /hyphen /registered /macron
180 /degree /plusminus /twosuperior /threesuperior
181 /acute /mu /paragraph /periodcentered
182 /cedilla /onesuperior /ordmasculine /guillemotright
183 /onequarter /onehalf /threequarters /questiondown
185 /Agrave /Aacute /Acircumflex /Atilde
186 /Adieresis /Aring /AE /Ccedilla
187 /Egrave /Eacute /Ecircumflex /Edieresis
188 /Igrave /Iacute /Icircumflex /Idieresis
190 /Eth /Ntilde /Ograve /Oacute
191 /Ocircumflex /Otilde /Odieresis /multiply
192 /Oslash /Ugrave /Uacute /Ucircumflex
193 /Udieresis /Yacute /Thorn /germandbls
195 /agrave /aacute /acircumflex /atilde
196 /adieresis /aring /ae /ccedilla
197 /egrave /eacute /ecircumflex /edieresis
198 /igrave /iacute /icircumflex /idieresis
200 /eth /ntilde /ograve /oacute
201 /ocircumflex /otilde /odieresis /divide
202 /oslash /ugrave /uacute /ucircumflex
203 /udieresis /yacute /thorn /ydieresis
208 %%BeginProcSet: lm-ec.enc 0 0
209 % This file belongs to the Latin Modern package. The work is released under
210 % the GUST Font License. See the MANIFEST.txt and README.eng files
211 % for the details. For the most recent version of this license see
212 % http://www.gust.org.pl/fonts/licenses/GUST-FONT-LICENSE.txt or
213 % http://tug.org/fonts/licenses/GUST-FONT-LICENSE.txt
475 %%BeginProcSet: texps.pro 0 0
477 TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
478 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
479 exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
480 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
481 pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
482 div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
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485 sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
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492 %%BeginProcSet: special.pro 0 0
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495 /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
496 /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
497 /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
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499 X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
500 /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
501 /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
502 {userdict/md get type/dicttype eq{userdict begin md length 10 add md
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504 /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
505 atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
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507 transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
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509 pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
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527 psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
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532 closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N
533 /@beginspecial{SDict begin/SpecialSave save N gsave normalscale
534 currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}
535 N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs
536 neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate
537 rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse
538 scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg
539 lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx
540 ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N
541 /setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{
542 pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave
543 restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B
544 /rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1
545 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY
546 moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix
547 matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc
548 savematrix setmatrix}N end
552 %!PS-AdobeFont-1.0: dsrom12 001.001
554 /FontInfo 16 dict dup begin
555 /version (001.001) readonly def
556 /Notice (Generated from MetaFont bitmap by pktrace, http://www.cs.uu.nl/~hanwen/pktrace/ ) readonly def
557 /FullName (dsrom12) readonly def
558 /FamilyName (dsrom12) readonly def
559 /Weight (Regular) readonly def
561 /isFixedPitch false def
562 /UnderlinePosition -100 def
563 /UnderlineThickness 50 def
565 /FontName /dsrom12 def
569 /FontMatrix [0.001000 0 0 0.001000 0 0] readonly def
570 /FontBBox {-46 -10 1025 901} readonly def
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618 %!PS-AdobeFont-1.1: CMMI8 1.100
619 %%CreationDate: 1996 Jul 23 07:53:54
620 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
622 /FontInfo 7 dict dup begin
623 /version (1.100) readonly def
624 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
625 /FullName (CMMI8) readonly def
626 /FamilyName (Computer Modern) readonly def
627 /Weight (Medium) readonly def
628 /ItalicAngle -14.04 def
629 /isFixedPitch false def
634 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
636 0 1 255 {1 index exch /.notdef put} for
640 /FontBBox{-24 -250 1110 750}readonly def
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698 %!PS-AdobeFont-1.1: CMR12 1.0
699 %%CreationDate: 1991 Aug 20 16:38:05
700 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
702 /FontInfo 7 dict dup begin
703 /version (1.0) readonly def
704 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
705 /FullName (CMR12) readonly def
706 /FamilyName (Computer Modern) readonly def
707 /Weight (Medium) readonly def
709 /isFixedPitch false def
714 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
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718 dup 41 /parenright put
726 /FontBBox{-34 -251 988 750}readonly def
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808 %!PS-AdobeFont-1.1: CMR8 1.0
809 %%CreationDate: 1991 Aug 20 16:39:40
810 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
812 /FontInfo 7 dict dup begin
813 /version (1.0) readonly def
814 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
815 /FullName (CMR8) readonly def
816 /FamilyName (Computer Modern) readonly def
817 /Weight (Medium) readonly def
819 /isFixedPitch false def
824 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
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830 /FontBBox{-36 -250 1070 750}readonly def
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882 %!PS-AdobeFont-1.1: CMMI12 1.100
883 %%CreationDate: 1996 Jul 27 08:57:55
884 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
886 /FontInfo 7 dict dup begin
887 /version (1.100) readonly def
888 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
889 /FullName (CMMI12) readonly def
890 /FamilyName (Computer Modern) readonly def
891 /Weight (Medium) readonly def
892 /ItalicAngle -14.04 def
893 /isFixedPitch false def
895 /FontName /CMMI12 def
898 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
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1225 %!PS-AdobeFont-1.1: CMSY10 1.0
1226 %%CreationDate: 1991 Aug 15 07:20:57
1227 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
1229 /FontInfo 7 dict dup begin
1230 /version (1.0) readonly def
1231 /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
1232 /FullName (CMSY10) readonly def
1233 /FamilyName (Computer Modern) readonly def
1234 /Weight (Medium) readonly def
1235 /ItalicAngle -14.035 def
1236 /isFixedPitch false def
1238 /FontName /CMSY10 def
1241 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
1243 0 1 255 {1 index exch /.notdef put} for
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1245 dup 21 /greaterequal put
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1247 dup 41 /arrowdblright put
1248 dup 44 /arrowdblboth put
1249 dup 54 /negationslash put
1250 dup 56 /universal put
1251 dup 57 /existential put
1252 dup 58 /logicalnot put
1253 dup 94 /logicaland put
1254 dup 95 /logicalor put
1255 dup 96 /turnstileleft put
1256 dup 102 /braceleft put
1257 dup 103 /braceright put
1260 /FontBBox{-29 -960 1116 775}readonly def
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1356 %%BeginFont: LMRoman12-Regular
1357 %!PS-AdobeFont-1.0: LMRoman12-Regular 1.010
1358 %%CreationDate: 16th January 2007
1359 % Generated by MetaType1 (a MetaPost-based engine)
1360 % Copyright 2003--2007 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).
1361 % Supported by CSTUG, DANTE eV, GUST, GUTenberg, NTG, and TUG.
1362 % METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki
1363 % from GUST (http://www.gust.org.pl).
1364 % This work is released under the GUST Font License.
1365 % For the most recent version of this license see
1366 % This work has the LPPL maintenance status `maintained'.
1367 % The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki.
1368 % This work consists of the files listed in the MANIFEST.txt file.
1371 FontDirectory/LMRoman12-Regular known{/LMRoman12-Regular findfont dup/UniqueID known{dup
1372 /UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse
1373 {save true}{false}ifelse}{false}ifelse
1375 /FontInfo 9 dict dup begin
1376 /version(1.010)readonly def
1377 /Notice(Copyright 2003--2007 by B. Jackowski and J.M. Nowacki (on behalf of TeX USERS GROUPS).)readonly def
1378 /FullName(LMRoman12-Regular)readonly def
1379 /FamilyName(LMRoman12)readonly def
1380 /Weight(Normal)readonly def
1381 /isFixedPitch false def
1383 /UnderlinePosition -175 def
1384 /UnderlineThickness 44 def
1386 /FontName /LMRoman12-Regular def
1388 0 1 255 {1 index exch /.notdef put} for
1394 /FontMatrix[0.001 0 0 0.001 0 0]readonly def
1396 /FontBBox{-422 -280 1394 1127}readonly def
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1897 TeXDict begin 1 0 bop -113 143 a Fs(P)m(artiel)44 b(de)g(math)937
1898 142 y(\264)927 143 y(ematiques)h(discr)2013 142 y(\036)2003
1899 143 y(etes,)f(semestre)h(2,)e(juin)g(2009.)1292 350 y(Dur)1569
1900 349 y(\264)1559 350 y(ee)i(:)e(3)g(heures.)1476 649 y
1901 Fq(C)6 b Fr(O)g(U)g(C)g(H)g(O)r(T)g Fq(,)36 b(J)6 b(.)g(-)g(F)l(.)-217
1902 1017 y Fp(Les)24 b(supports)g(de)h(TDs)f(et)h(de)g(TP)g(sont)f(autoris)
1903 6 b(\264)-39 b(es)16 b(;)25 b(t)6 b(\264)-39 b(el)6 b(\264)-39
1904 b(ephones)24 b(et)g(calculatrices)h(sont)f(interdits.)-364
1905 1355 y Fo(1)143 b(QCM)36 b(\(1h45\))-217 1578 y Fp(Q.)24
1906 b(1.)h(L)-9 b('af)n(\002rmation)24 b Fn(\023)c Fp(il)k(f)o(ait)h(beau)g
1907 (aujourd'hui)f(donc)g(il)h(ne)g(pleuvra)f(pas)h(dans)g(dix)f(jours)19
1908 b Fn(\024)25 b Fp(est-elle)g(une)f(proposition)15 b(?)-217
1909 1699 y(Q.)24 b(2.)h(Soit)f(la)h(d)6 b(\264)-39 b(emonstration)23
1910 b(syntaxique)h(sui)n(v)n(ante)f(:)-314 1813 y(D)6 b(\264)-39
1911 b(emonstration)-314 1933 y(1.)99 b Fm(:)p Fl(B)34 b Fm(\))27
1912 b(:)p Fl(A)106 b(H)487 1948 y Fk(1)-314 2054 y Fp(2.)99
1913 b Fl(A)473 b(H)487 2069 y Fk(2)-314 2174 y Fp(3.)p -134
1914 2174 30 4 v -98 2174 V -62 2174 V -26 2174 V 10 2174
1915 V 412 2174 V 448 2174 V 484 2174 V 520 2174 V 556 2174
1916 V -314 2294 a(4.)p -134 2294 V -98 2294 V -62 2294 V
1917 -26 2294 V 10 2294 V 412 2294 V 448 2294 V 484 2294 V
1918 520 2294 V 556 2294 V -314 2415 a(5.)99 b Fm(::)p Fl(B)340
1919 b Fp(r)6 b(\264)-39 b(eduction)24 b(de)h(l'absurde)g(entre)g(4.)g(et)f
1920 (1.)-314 2535 y(6.)99 b Fm(::)p Fl(B)34 b Fm(\))27 b
1921 Fl(B)105 b Fp(Axiome)24 b(9.)-314 2655 y(7.)99 b(B)480
1922 b(mp)24 b(entre)h(5.)g(et)g(6.)1892 2235 y(La)g(d)6 b(\264)-39
1923 b(emonstration)23 b(est)h(correcte)i(si)e(en)h(3.)g(et)g(4.)f(on)h(a)g
1924 (:)-314 2784 y(3.)99 b Fm(::)p Fl(A)29 b Fm(\))e(::)p
1925 Fl(B)106 b Fp(th)6 b(\264)-39 b(eoreme)25 b(de)f(la)h(contrapos)6
1926 b(\264)-39 b(ee)25 b(sur)g(1.)-314 2904 y(4.)99 b Fm(::)p
1927 Fl(A)29 b Fm(\))e Fl(A)239 b Fp(Axiome)24 b(9.)-217 3086
1928 y(Q.)e(3.)g Fn(\023)c Fj(Si)k(la)g(paix)h(survient,)e(alor)o(s)g(il)h
1929 (y)h(aur)o(a)e(une)i(crise)1802 3087 y(\264)1797 3086
1930 y(economique)2309 3087 y(\036)2301 3086 y(a)f(moins)g(que)g(le)g(pays)h
1931 (se)f(dote)g(d'armes)g(nouvelles)-364 3206 y(ou)28 b(bien)g(e)n(x)55
1932 3207 y(\264)50 3206 y(ecute)h(un)f(lar)l(g)o(e)g(pr)l(o)o(gr)o(amme)e
1933 (d'in)l(vestissement)h(int)1931 3207 y(\264)1926 3206
1934 y(erieur)g(dans)h(les)g(secteur)o(s)g(de)g(l'enseignement,)g(de)g(la)g
1935 (sant)4086 3207 y(\264)4081 3206 y(e)-364 3327 y(et)h(de)g(la)g(lutte)f
1936 (contr)l(e)h(la)f(pauvr)l(et)865 3328 y(\264)860 3327
1937 y(e.)h(Il)g(n'est)g(pas)f(possible)g(de)h(se)g(mettr)l(e)g(d'accor)l(d)
1938 g(sur)f(les)h(objectifs)f(que)h(peut)f(se)h(donner)-364
1939 3447 y(un)g(lar)l(g)o(e)f(pr)l(o)o(gr)o(amme)e(d'in)l(vestissement)i
1940 (int)1280 3448 y(\264)1275 3447 y(erieur)-11 b(.)27 b(Donc)h(si)g(la)g
1941 (paix)h(survient)e(et)i(qu'il)f(n'y)h(a)f(pas)g(de)h(crise)3624
1942 3448 y(\264)3619 3447 y(economique)o(,)-364 3567 y(le)c(pays)g(doit)e
1943 (se)i(doter)g(d'armes)f(nouvelles.)19 b Fn(\024)25 b
1944 Fp(Le)g(raisonnement)f(propos)6 b(\264)-39 b(e)24 b(est-il)g(correct)18
1945 b(?)-217 3688 y(Q.)24 b(4.)h(La)g(relation)f Fm(f)p Fl(P)s(;)17
1946 b(Q)p Fm(g)27 b(`)h Fl(R)e Fp(se)e(lit-elle)g Fn(\023)d
1947 Fl(R)26 b Fp(est)e(une)h(cons)6 b(\264)-39 b(equence)25
1948 b(logique)f(de)h(l'ensemble)f Fm(f)p Fl(P)s(;)17 b(Q)p
1949 Fm(g)i Fn(\024)e Fp(?)-217 3808 y(Q.)24 b(5.)h(Soit)f
1950 Fl(p)p Fp(,)h Fl(q)t Fp(,)f Fl(r)k Fp(trois)c(v)n(ariables)g
1951 (propostionnelles.)e(L)-9 b(')6 b(\264)-39 b(enonc)6
1952 b(\264)-39 b(e)25 b(sui)n(v)n(ant)d(est-il)i(une)h(tautologie)15
1953 b(?)25 b Fi(\()p Fl(p)d Fm(_)g Fl(q)t Fi(\))g Fm(^)g
1954 Fi(\()p Fl(p)f Fm(_)i Fl(r)s Fi(\))k Fm(\))-364 3929
1955 y Fl(p)22 b Fm(_)h Fi(\()p Fl(q)j Fm(^)c Fl(r)s Fi(\))p
1956 Fp(.)-217 4049 y(Q.)41 b(6.)h(Soit)f Fl(p)g Fp(et)h Fl(q)t
1957 Fp(,)f(deux)h(v)n(ariables)e(propostionnelles.)g(L)-9
1958 b(')6 b(\264)-39 b(enonc)6 b(\264)-39 b(e)41 b(sui)n(v)n(ant)f(est-il)h
1959 (une)g(tautologie)15 b(?)42 b Fi(\()p Fl(p)59 b Fm(\))f
1960 Fl(q)t Fi(\))h Fm(\))-364 4169 y Fi(\(\()p Fl(q)32 b
1961 Fm(\))27 b Fl(p)p Fi(\))g Fm(\))h Fi(\()p Fl(q)j Fm(,)c
1962 Fl(p)p Fi(\)\))p Fp(.)-217 4290 y(Q.)34 b(7.)f(La)i(formule)e
1963 Fm(8)p Fl(x)17 b(:)g(x)45 b(>)g Fi(0)g Fm(\))f Fi(\()p
1964 Fm(9)p Fl(y)20 b(:)d(e)1391 4254 y Fh(y)1477 4290 y Fi(=)45
1965 b Fl(x)p Fi(\))34 b Fp(est)g(vraie)g(sur)g(l'uni)n(v)o(ers)e
1966 Fg(R)p Fp(.)j(L)-9 b('assertion)33 b(propos)6 b(\264)-39
1967 b(ee)34 b(est)g(vraie)g(ou)-364 4410 y(f)o(ausse)17 b(?)-217
1968 4530 y(Q.)24 b(8.)h Fn(\023)20 b Fl(A)31 b Fp(\036)-39
1969 b(a)25 b(moins)f(que)g Fl(B)i Fn(\024)f Fp(peut-elle)30
1970 b(\210)-39 b(etre)25 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39
1971 b(ee)26 b(par)f Fm(:)p Fl(A)j Fm(\))g Fl(B)21 b Fp(?)-217
1972 4651 y(Q.)28 b(9.)h(Soit)g Fl(x)g Fp(et)g Fl(y)j Fp(des)d(entiers)f
1973 (naturels.)g Fm(9)p Fl(x)17 b(:)g Fi(\()p Fm(8)p Fl(y)j(:)d(y)38
1974 b Fm(6)p Fi(=)d Fl(x)h Fm(\))f Fl(x)g(<)g Fi(1\))29 b
1975 Fp(est)g(vraie.)g(L)-9 b('assertion)28 b(propos)6 b(\264)-39
1976 b(ee)28 b(est)h(vraie)g(ou)-364 4771 y(f)o(ausse)17 b(?)-217
1977 4892 y(Q.)24 b(10.)h(Soit)f Fl(f)11 b Fp(,)25 b Fl(g)j
1978 Fp(des)d(symboles)e(de)i(fonctions)f(binaire,)g Fl(R)i
1979 Fp(un)f(symbole)e(de)i(relation)f(binaire.)h(Soit)f Fl(A)h
1980 Fp(la)g(formule)834 5103 y Fi(\()p Fm(8)p Fl(z)c(:)c(R)q
1981 Fi(\()p Fl(x;)g(z)t Fi(\))23 b Fm(^)g Fl(R)q Fi(\()p
1982 Fl(z)t(;)17 b(y)t Fi(\)\))27 b Fm(\))g Fi(\()p Fm(9)p
1983 Fl(z)22 b(:)17 b(R)q Fi(\()p Fl(z)t(;)g(y)t Fi(\))k Fm(_)i
1984 Fl(R)q Fi(\()p Fl(x;)17 b(z)t Fi(\)\))g Fl(:)-364 5314
1985 y Fp(Soit)25 b Fl(u)p Fp(,)f Fl(v)29 b Fp(les)24 b(termes)h(d)6
1986 b(\264)-39 b(e\002nis)24 b(par)i Fl(u)h Fi(=)g Fl(f)11
1987 b Fi(\()p Fl(z)t(;)17 b(x)p Fi(\))26 b Fp(et)e Fl(v)32
1988 b Fi(=)27 b Fl(g)t Fi(\()p Fl(x;)17 b(z)t Fi(\))-217
1989 5434 y Fp(Alors)24 b(on)g(a)1161 5554 y Fl(A)p Fi(\()p
1990 Fl(v)t(=y)t Fi(\)\()p Fl(u=x)p Fi(\))i Fm(\021)i Fl(A)p
1991 Fi(\()p Fl(u=x)p Fi(\)\()p Fl(v)t Fi(\()p Fl(u=x)p Fi(\))p
1992 Fl(=y)t Fi(\))-364 5725 y Fp(L)-9 b('assertion)24 b(propos)6
1993 b(\264)-39 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16
1994 b(?)-217 5845 y(Q.)24 b(11.)h(Soit)f Fl(p)p Fp(,)h Fl(q)t
1995 Fp(,)g Fl(r)i Fp(trois)d(v)n(ariables)g(propostionnelles.)f(La)i
1996 (relation)f Fm(f)p Fl(p)j Fm(\))h(:)p Fl(q)t(;)17 b(q)t
1997 Fm(g)27 b(j)-17 b Fi(=)28 b Fm(:)p Fl(p)d Fp(est-elle)g(vraie)16
1998 b(?)-217 5946 y(Q.)24 b(12.)h(Dans)f(les)h(clauses)-364
1999 6101 y Ff(pere_de\(Y,Z\))38 b(:-)i(homme\(Y\),a_pour_fils\(Y,Z\).)-364
2000 6180 y(pere_de\(Y,Z\))e(:-)i(homme\(Y\),a_pour_fille\(Y,Z\).)1855
2001 6429 y Fp(1)p eop end
2003 TeXDict begin 2 1 bop -217 -264 a Fp(La)25 b(premi)6
2004 b(\036)-39 b(ere)25 b(clause)f(se)h(traduit)f(en)876
2005 -44 y Fm(8)p Fl(y)t(;)17 b(z)k(:)c Fj(per)l(e)p Fi(\()p
2006 Fl(y)t(;)g(z)t Fi(\))27 b Fm(,)g Fj(homme)p Fi(\()p Fl(y)t
2007 Fi(\))21 b Fm(^)i Fj(a)p 2267 -44 30 4 v 35 w(pour)p
2008 2491 -44 V 36 w(\002ls)o Fi(\()p Fl(y)t(;)17 b(z)t Fi(\))p
2009 Fl(:)-364 176 y Fp(L)-9 b('assertion)24 b(propos)6 b(\264)-39
2010 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16 b(?)-217 296
2011 y(Q.)24 b(13.)h Fn(\023)20 b Fl(A)30 b Fp(\036)-38 b(a)25
2012 b(moins)f(que)g Fl(B)h Fn(\024)g Fp(peut-elle)30 b(\210)-38
2013 b(etre)25 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39 b(ee)26
2014 b(par)f Fm(:)p Fl(B)j Fm(_)22 b Fl(A)17 b Fp(?)-217 417
2015 y(Q.)h(14.)h(Soit)f Fl(p)h Fp(et)g Fl(q)t Fp(,)g(deux)f(v)n(ariables)g
2016 (propostionnelles.)f(L)-9 b(')6 b(\264)-39 b(enonc)6
2017 b(\264)-39 b(e)19 b(sui)n(v)n(ant)e(est-il)h(une)h(tautologie)c(?)k
2018 Fi(\(\()p Fl(p)27 b Fm(\))h Fl(q)t Fi(\))f Fm(\))g Fi(\()p
2019 Fl(q)32 b Fm(\))27 b Fl(p)p Fi(\)\))h Fm(\))-364 537
2020 y Fi(\()p Fl(q)k Fm(,)27 b Fl(p)p Fi(\))p Fp(.)-217 657
2021 y(Q.)34 b(15.)g(On)h(consid)6 b(\036)-39 b(ere)34 b(les)h(pr)6
2022 b(\264)-39 b(edicats)34 b(Prolog)g Fe(parent\(X,Y\))p
2023 Fp(,)f(qui)h(est)g(vrai)h(si)f Fe(X)g Fp(est)h(le)f(p)6
2024 b(\036)-39 b(ere)35 b(ou)g(la)f(m)6 b(\036)-39 b(ere)35
2025 b(de)g Fe(Y)f Fp(et)-364 778 y Fe(femme\(X\))p Fp(,)23
2026 b(qui)h(est)h(vrai)g(si)f Fe(X)h Fp(est)g(est)f(une)h(femme.)-217
2027 876 y Fn(\023)20 b Fe(X)k Fp(est)h(la)g(soeur)f(de)h
2028 Fe(Y)20 b Fn(\024)25 b Fp(se)g(traduit)f(en)h(prolog)f(par)-364
2029 1037 y Ff(est_la_soeur_de\(X,Y\))37 b(:-)j(parent\(Z,X\),)e
2030 (parent\(Z,Y\),)g(femme\(X\).)-217 1241 y Fp(L)-9 b('assertion)23
2031 b(propos)6 b(\264)-39 b(ee)25 b(est)g(vraie)g(ou)f(f)o(ausse)17
2032 b(?)-217 1361 y(Q.)23 b(16.)g Fn(\023)c Fp(Il)24 b(est)f(f)o(aux)h(que)
2033 f(sa)h(m)6 b(\036)-39 b(ere)24 b(est)f(anglaise)g(ou)g(que)h(son)f(p)6
2034 b(\036)-39 b(ere)24 b(est)f(franc)-38 b(\270)6 b(ais)18
2035 b Fn(\024)24 b Fp(est-elle)f(suf)n(\002sante)g(pour)h(af)n(\002rmer)g
2036 (que)-364 1482 y Fn(\023)c Fp(sa)25 b(m)6 b(\036)-39
2037 b(ere)25 b(est)g(anglaise)f(ou)h(son)f(p)6 b(\036)-39
2038 b(ere)25 b(n'est)g(pas)g(franc)-38 b(\270)5 b(ais)20
2039 b Fn(\024)d Fp(?)-217 1602 y(Q.)34 b(17.)g(On)h(consid)6
2040 b(\036)-39 b(ere)34 b(les)h(pr)6 b(\264)-39 b(edicats)34
2041 b(Prolog)g Fe(parent\(X,Y\))p Fp(,)f(qui)h(est)g(vrai)h(si)f
2042 Fe(X)g Fp(est)h(le)f(p)6 b(\036)-39 b(ere)35 b(ou)g(la)f(m)6
2043 b(\036)-39 b(ere)35 b(de)g Fe(Y)f Fp(et)-364 1722 y Fe(femme\(X\))p
2044 Fp(,)23 b(qui)h(est)h(vrai)g(si)f Fe(X)h Fp(est)g(est)f(une)h(femme.)
2045 -217 1820 y Fn(\023)20 b Fe(X)k Fp(est)h(la)g(\002lle)g(de)g
2046 Fe(Y)19 b Fn(\024)25 b Fp(se)g(traduit)f(en)h(prolog)f(par)-364
2047 1982 y Ff(fille\(X,Y\))39 b(:-)g(parent\(X,Y\),)f(femme\(X\).)-217
2048 2186 y Fp(L)-9 b('assertion)23 b(propos)6 b(\264)-39
2049 b(ee)25 b(est)g(vraie)g(ou)f(f)o(ausse)17 b(?)-217 2306
2050 y(Q.)30 b(18.)h(Dans)g(la)f(formule)h Fi(\()p Fm(8)p
2051 Fl(x)17 b(:)g(x)39 b Fm(\025)h Fi(5\))26 b Fm(^)h Fi(\()p
2052 Fm(9)p Fl(y)20 b(:)d(y)42 b Fm(\025)d Fl(x)p Fi(\))31
2053 b Fp(la)g(v)n(ariable)g Fl(x)g Fp(est)g(li)6 b(\264)-39
2054 b(ee.)30 b(L)-9 b('assertion)30 b(propos)6 b(\264)-39
2055 b(ee)31 b(est)g(vraie)g(ou)-364 2426 y(f)o(ausse)17 b(?)-217
2056 2547 y(Q.)k(19.)g(On)g(note)h Fl(A)f Fp(la)h(proposition)d
2057 Fn(\023)f Fp(les)j(chiens)g(aboient)c Fn(\024)k Fp(et)h
2058 Fl(P)35 b Fp(la)22 b(proposition)d Fn(\023)e Fp(la)22
2059 b(cara)n(v)n(ane)g(passe)17 b Fn(\024)p Fp(.)22 b(La)g(proposition)-364
2060 2667 y Fn(\023)e Fp(les)25 b(chiens)f(aboient)30 b(\036)-38
2061 b(a)25 b(moins)e(que)i(la)g(cara)n(v)n(ane)g(ne)g(passe)20
2062 b Fn(\024)25 b Fp(peut-elle)30 b(\210)-39 b(etre)26 b(repr)6
2063 b(\264)-39 b(esent)6 b(\264)-39 b(ee)25 b(par)g Fm(:)p
2064 Fl(P)42 b Fm(\))27 b Fl(A)17 b Fp(?)-217 2787 y(Q.)24
2065 b(20.)h(Soit)f Fl(p)p Fp(,)h Fl(q)t Fp(,)g Fl(r)i Fp(trois)d(v)n
2066 (ariables)g(propostionnelles.)f(La)i(relation)f Fm(f)p
2067 Fl(r)s Fm(g)j(j)-17 b Fi(=)28 b Fl(p)22 b Fm(^)g Fl(q)32
2068 b Fm(\))27 b Fl(r)h Fp(est-elle)c(vraie)17 b(?)-217 2908
2069 y(Q.)33 b(21.)h(Soit)g Fl(a)g Fp(et)g Fl(b)h Fp(des)e(symboles)g(de)h
2070 (constante,)f Fl(f)45 b Fp(un)34 b(symbole)e(de)i(fonction)g(unaire,)g
2071 Fl(g)j Fp(un)d(symbole)e(de)i(fonction)-364 3028 y(binaire)25
2072 b(et)g Fl(S)30 b Fp(un)25 b(symbole)e(de)i(relation)g(binaire.)f(On)h
2073 (donne)f(les)h(e)o(xpressions)e(sui)n(v)n(antes)g(:)-243
2074 3184 y(1.)48 b Fl(g)t Fi(\()p Fl(a;)17 b(f)11 b Fi(\()p
2075 Fl(b)p Fi(\)\))-243 3341 y Fp(2.)48 b Fl(S)6 b Fi(\()p
2076 Fl(f)11 b Fi(\()p Fl(a)p Fi(\))p Fl(;)17 b(g)t Fi(\()p
2077 Fl(x;)g(f)11 b Fi(\()p Fl(y)t Fi(\)\)\))-217 3497 y Fp(L)-9
2078 b('e)o(xpression)23 b(1)i(contient)f(1)g(seul)h(terme)f(L)-9
2079 b('assertion)24 b(propos)6 b(\264)-39 b(ee)25 b(est)g(vraie)g(ou)f(f)o
2080 (ausse)17 b(?)-217 3617 y(Q.)39 b(22.)h(On)f(consid)6
2081 b(\036)-39 b(ere)40 b(les)f(pr)6 b(\264)-39 b(edicats)40
2082 b(et)f(constantes)g(sui)n(v)n(ants)f(a)n(v)o(ec)h(leur)h(interpr)6
2083 b(\264)-39 b(etation)39 b(sur)g(un)h(uni)n(v)o(ers)e(constitu)6
2084 b(\264)-39 b(e)-364 3738 y(d'indi)n(vidus)23 b(humains.)p
2085 1172 3857 1417 4 v 1172 3976 4 121 v 1402 3940 a(pr)6
2086 b(\264)-39 b(edicat)p 1772 3976 V 103 w(sens)p 2585 3976
2087 V 1172 3977 1417 4 v 1172 4096 4 121 v 1303 4060 a Fj(aime)o
2088 Fi(\()p Fl(x;)17 b(y)t Fi(\))p 1772 4096 V 103 w Fl(x)25
2089 b Fp(aime)f Fl(y)p 2585 4096 V 1172 4216 V 1225 4180
2090 a Fj(maries)o Fi(\()p Fl(x;)17 b(y)t Fi(\))p 1772 4216
2091 V 103 w Fl(x)25 b Fp(et)g Fl(y)j Fp(sont)c(mari)6 b(\264)-39
2092 b(es)p 2585 4216 V 1172 4337 V 1331 4301 a Fj(femme)p
2093 Fi(\()p Fl(x)p Fi(\))p 1772 4337 V 104 w Fl(x)25 b Fp(est)f(une)h
2094 (femme)p 2585 4337 V 1172 4457 V 1304 4421 a Fj(homme)o
2095 Fi(\()p Fl(x)p Fi(\))p 1772 4457 V 104 w Fl(x)g Fp(est)f(un)h(homme)p
2096 2585 4457 V 1172 4578 V 1376 4542 a Fj(\002dele)o Fi(\()p
2097 Fl(x)p Fi(\))p 1772 4578 V 104 w Fl(x)g Fp(est)f(\002d)6
2098 b(\036)-39 b(ele)p 2585 4578 V 1172 4698 V 1326 4662
2099 a Fj(honete)o Fi(\()p Fl(x)p Fi(\))p 1772 4698 V 104
2100 w Fl(x)25 b Fp(dit)f(la)h(v)6 b(\264)-39 b(erit)6 b(\264)-39
2101 b(e)p 2585 4698 V 1172 4818 V 1671 4782 a Fl(a)p 1772
2102 4818 V 104 w Fp(Alice)p 2585 4818 V 1172 4939 V 1681
2103 4903 a Fl(b)p 1772 4939 V 104 w Fp(Bob)p 2585 4939 V
2104 1172 5059 V 1681 5023 a Fl(c)p 1772 5059 V 103 w Fp(Clinton)p
2105 2585 5059 V 1172 5061 1417 4 v -217 5244 a Fn(\023)20
2106 b Fp(L)-9 b(')6 b(\264)-39 b(epoux)24 b(qui)g(aime)h(son)30
2107 b(\264)-39 b(epouse)25 b(lui)f(est)g(\002d)6 b(\036)-39
2108 b(ele)21 b Fn(\024)p Fp(peut)j(se)h(traduire)g(en)454
2109 5485 y Fm(8)p Fl(x;)17 b(y)k(:)c Fj(homme)o Fi(\()p Fl(x)p
2110 Fi(\))23 b Fm(^)f Fj(femme)p Fi(\()p Fl(y)t Fi(\))f Fm(^)i
2111 Fj(maries)o Fi(\()p Fl(x;)17 b(y)t Fi(\))k Fm(^)i Fj(aime)p
2112 Fi(\()p Fl(x;)17 b(y)t Fi(\))k Fm(^)h Fj(aime)p Fi(\()p
2113 Fl(y)t(;)17 b(x)p Fi(\))-217 5659 y Fp(L)-9 b('assertion)23
2114 b(propos)6 b(\264)-39 b(ee)25 b(est)g(vraie)g(ou)f(f)o(ausse)17
2115 b(?)-217 5779 y(Q.)39 b(23.)h(On)f(consid)6 b(\036)-39
2116 b(ere)40 b(les)f(pr)6 b(\264)-39 b(edicats)40 b(et)f(constantes)g(sui)n
2117 (v)n(ants)f(a)n(v)o(ec)h(leur)h(interpr)6 b(\264)-39
2118 b(etation)39 b(sur)g(un)h(uni)n(v)o(ers)e(constitu)6
2119 b(\264)-39 b(e)-364 5900 y(d'indi)n(vidus)23 b(humains.)1855
2122 TeXDict begin 3 2 bop 1172 -362 1417 4 v 1172 -243 4
2123 121 v 1402 -280 a Fp(pr)6 b(\264)-39 b(edicat)p 1772
2124 -243 V 103 w(sens)p 2585 -243 V 1172 -242 1417 4 v 1172
2125 -123 4 121 v 1303 -159 a Fj(aime)o Fi(\()p Fl(x;)17 b(y)t
2126 Fi(\))p 1772 -123 V 103 w Fl(x)25 b Fp(aime)f Fl(y)p
2127 2585 -123 V 1172 -3 V 1225 -39 a Fj(maries)o Fi(\()p
2128 Fl(x;)17 b(y)t Fi(\))p 1772 -3 V 103 w Fl(x)25 b Fp(et)g
2129 Fl(y)j Fp(sont)c(mari)6 b(\264)-39 b(es)p 2585 -3 V 1172
2130 118 V 1331 82 a Fj(femme)p Fi(\()p Fl(x)p Fi(\))p 1772
2131 118 V 104 w Fl(x)25 b Fp(est)f(une)h(femme)p 2585 118
2132 V 1172 238 V 1304 202 a Fj(homme)o Fi(\()p Fl(x)p Fi(\))p
2133 1772 238 V 104 w Fl(x)g Fp(est)f(un)h(homme)p 2585 238
2134 V 1172 359 V 1376 322 a Fj(\002dele)o Fi(\()p Fl(x)p
2135 Fi(\))p 1772 359 V 104 w Fl(x)g Fp(est)f(\002d)6 b(\036)-39
2136 b(ele)p 2585 359 V 1172 479 V 1326 443 a Fj(honete)o
2137 Fi(\()p Fl(x)p Fi(\))p 1772 479 V 104 w Fl(x)25 b Fp(dit)f(la)h(v)6
2138 b(\264)-39 b(erit)6 b(\264)-39 b(e)p 2585 479 V 1172
2139 599 V 1671 563 a Fl(a)p 1772 599 V 104 w Fp(Alice)p 2585
2140 599 V 1172 720 V 1681 684 a Fl(b)p 1772 720 V 104 w Fp(Bob)p
2141 2585 720 V 1172 840 V 1681 804 a Fl(c)p 1772 840 V 103
2142 w Fp(Clinton)p 2585 840 V 1172 842 1417 4 v -217 1019
2143 a Fn(\023)20 b Fp(Les)k(femmes)h(aiment)f(toujours)f(les)i(hommes)e
2144 (\002d)6 b(\036)-39 b(eles)25 b(et)g(qui)g(disent)e(la)i(v)6
2145 b(\264)-39 b(erit)6 b(\264)-39 b(e)20 b Fn(\024)p Fp(peut)25
2146 b(se)g(traduire)f(en)481 1260 y Fm(8)p Fl(x;)17 b(y)j(:)d
2147 Fi(\()p Fj(homme)p Fi(\()p Fl(x)p Fi(\))22 b Fm(^)h Fj(femme)p
2148 Fi(\()p Fl(y)t Fi(\))e Fm(^)h Fj(\002dele)p Fi(\()p Fl(x)p
2149 Fi(\))g Fm(^)h Fj(honete)p Fi(\()p Fl(x)p Fi(\)\))28
2150 b Fm(\))f Fj(aime)p Fi(\()p Fl(y)t(;)17 b(x)p Fi(\))-217
2151 1432 y Fp(L)-9 b('assertion)23 b(propos)6 b(\264)-39
2152 b(ee)25 b(est)g(vraie)g(ou)f(f)o(ausse)17 b(?)-217 1553
2153 y(Q.)39 b(24.)h(On)f(consid)6 b(\036)-39 b(ere)40 b(les)f(pr)6
2154 b(\264)-39 b(edicats)40 b(et)f(constantes)g(sui)n(v)n(ants)f(a)n(v)o
2155 (ec)h(leur)h(interpr)6 b(\264)-39 b(etation)39 b(sur)g(un)h(uni)n(v)o
2156 (ers)e(constitu)6 b(\264)-39 b(e)-364 1673 y(d'indi)n(vidus)23
2157 b(humains.)p 1172 1787 V 1172 1906 4 121 v 1402 1870
2158 a(pr)6 b(\264)-39 b(edicat)p 1772 1906 V 103 w(sens)p
2159 2585 1906 V 1172 1907 1417 4 v 1172 2026 4 121 v 1303
2160 1990 a Fj(aime)o Fi(\()p Fl(x;)17 b(y)t Fi(\))p 1772
2161 2026 V 103 w Fl(x)25 b Fp(aime)f Fl(y)p 2585 2026 V 1172
2162 2146 V 1225 2110 a Fj(maries)o Fi(\()p Fl(x;)17 b(y)t
2163 Fi(\))p 1772 2146 V 103 w Fl(x)25 b Fp(et)g Fl(y)j Fp(sont)c(mari)6
2164 b(\264)-39 b(es)p 2585 2146 V 1172 2267 V 1331 2231 a
2165 Fj(femme)p Fi(\()p Fl(x)p Fi(\))p 1772 2267 V 104 w Fl(x)25
2166 b Fp(est)f(une)h(femme)p 2585 2267 V 1172 2387 V 1304
2167 2351 a Fj(homme)o Fi(\()p Fl(x)p Fi(\))p 1772 2387 V
2168 104 w Fl(x)g Fp(est)f(un)h(homme)p 2585 2387 V 1172 2508
2169 V 1376 2471 a Fj(\002dele)o Fi(\()p Fl(x)p Fi(\))p 1772
2170 2508 V 104 w Fl(x)g Fp(est)f(\002d)6 b(\036)-39 b(ele)p
2171 2585 2508 V 1172 2628 V 1326 2592 a Fj(honete)o Fi(\()p
2172 Fl(x)p Fi(\))p 1772 2628 V 104 w Fl(x)25 b Fp(dit)f(la)h(v)6
2173 b(\264)-39 b(erit)6 b(\264)-39 b(e)p 2585 2628 V 1172
2174 2748 V 1671 2712 a Fl(a)p 1772 2748 V 104 w Fp(Alice)p
2175 2585 2748 V 1172 2869 V 1681 2833 a Fl(b)p 1772 2869
2176 V 104 w Fp(Bob)p 2585 2869 V 1172 2989 V 1681 2953 a
2177 Fl(c)p 1772 2989 V 103 w Fp(Clinton)p 2585 2989 V 1172
2178 2991 1417 4 v 909 3220 a Fm(9)p Fl(x)17 b(:)g Fi(\()p
2179 Fm(8)p Fl(y)j(:)d Fj(homme)o Fi(\()p Fl(x)p Fi(\))23
2180 b Fm(^)f Fi(\()p Fj(femme)p Fi(\()p Fl(y)t Fi(\))27 b
2181 Fm(\))g Fj(aime)p Fi(\()p Fl(x;)17 b(y)t Fi(\)\))-217
2182 3393 y Fp(peut)24 b(se)h(traduire)g(en)g Fn(\023)20 b
2183 Fp(certains)k(hommes)g(sont)g(aim)6 b(\264)-39 b(es)24
2184 b(de)h(toutes)f(les)h(femmes)19 b Fn(\024)p Fp(.)-217
2185 3513 y(L)-9 b('assertion)23 b(propos)6 b(\264)-39 b(ee)25
2186 b(est)g(vraie)g(ou)f(f)o(ausse)17 b(?)-217 3633 y(Q.)24
2187 b(25.)h(L)-9 b('af)n(\002rmation)24 b Fn(\023)c Fp(le)25
2188 b(V)-11 b(esuv)o(e)24 b(a)h(ra)n(v)n(ag)6 b(\264)-39
2189 b(e)25 b(la)g(ville)f(de)h(Pompei)f(en)h(1999)19 b Fn(\024)25
2190 b Fp(est-elle)g(une)g(proposition)14 b(?)-217 3754 y(Q.)21
2191 b(26.)h(Soit)f Fj(dodec)h Fp(le)g(pr)6 b(\264)-39 b(edicat)22
2192 b(unaire)g(qui)f(est)g(vrai)h(si)g(son)f(param)6 b(\036)-39
2193 b(etre)22 b(est)g(un)f(dod)6 b(\264)-39 b(eca)6 b(\036)-39
2194 b(edre,)23 b Fj(cube)f Fp(le)f(pr)6 b(\264)-39 b(edicat)22
2195 b(unaire)g(qui)-364 3874 y(est)f(vrai)h(si)f(son)g(param)6
2196 b(\036)-39 b(etre)21 b(est)h(un)f(cube,)g Fj(petit)i
2197 Fp(le)e(pr)6 b(\264)-39 b(edicat)21 b(unaire)h(qui)f(est)g(vrai)g(si)g
2198 (son)g(param)6 b(\036)-39 b(etre)22 b(est)f(petit,)g
2199 Fj(entr)l(e)g Fp(le)h(pr)6 b(\264)-39 b(edicat)-364 3994
2200 y(ternaire)24 b(qui)e(est)h(vrai)g(si)g(son)f(premier)i(param)6
2201 b(\036)-39 b(etre)23 b(est)g(entre)g(le)g(second)g(et)g(le)h(troisi)6
2202 b(\036)-39 b(eme)22 b(et)h Fj(de)o(vant)h Fp(le)f(pr)6
2203 b(\264)-39 b(edicat)23 b(unaire)g(qui)g(est)-364 4115
2204 y(vrai)i(si)f(son)h(premier)f(param)6 b(\036)-39 b(etre)26
2205 b(est)e(de)n(v)n(ant)g(son)g(second)h(param)6 b(\036)-39
2206 b(etre.)-217 4235 y Fn(\023)20 b Fp(si)k(un)h(cube)g(a)g(quelque)f
2207 (chose)h(de)n(v)n(ant)e(lui)h(alors)h(il)f(est)h(petit)19
2208 b Fn(\024)25 b Fp(peut-elle)g(se)f(traduire)h(en)960
2209 4450 y Fm(8)p Fl(x)17 b(:)g Fi(\()p Fm(9)p Fl(y)j(:)d(cube)p
2210 Fi(\()p Fl(x)p Fi(\))22 b Fm(^)h Fl(dev)t(ant)p Fi(\()p
2211 Fl(x;)17 b(y)t Fi(\)\))27 b Fm(\))g Fl(petit)p Fi(\()p
2212 Fl(x)p Fi(\))-364 4666 y Fp(L)-9 b('assertion)24 b(propos)6
2213 b(\264)-39 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16
2214 b(?)-217 4786 y(Q.)27 b(27.)f(Soit)h Fl(p)p Fp(,)g Fl(q)t
2215 Fp(,)g Fl(r)j Fp(trois)c(v)n(ariables)h(propostionnelles.)d(L)-9
2216 b(')6 b(\264)-39 b(enonc)6 b(\264)-39 b(e)27 b(sui)n(v)n(ant)f(est-il)g
2217 (une)h(tautologie)15 b(?)28 b Fi(\()p Fl(q)35 b Fm(,)d
2218 Fl(p)p Fi(\))f Fm(\))h Fi(\()p Fl(p)g Fm(\))-364 4906
2219 y Fl(q)t Fi(\))22 b Fm(^)h Fi(\()p Fl(q)31 b Fm(\))c
2220 Fl(p)p Fi(\))p Fp(.)-217 5027 y(Q.)21 b(28.)h(Soit)f
2221 Fj(dodec)h Fp(le)g(pr)6 b(\264)-39 b(edicat)22 b(unaire)g(qui)f(est)g
2222 (vrai)h(si)g(son)f(param)6 b(\036)-39 b(etre)22 b(est)g(un)f(dod)6
2223 b(\264)-39 b(eca)6 b(\036)-39 b(edre,)23 b Fj(cube)f
2224 Fp(le)f(pr)6 b(\264)-39 b(edicat)22 b(unaire)g(qui)-364
2225 5147 y(est)f(vrai)h(si)f(son)g(param)6 b(\036)-39 b(etre)21
2226 b(est)h(un)f(cube,)g Fj(petit)i Fp(le)e(pr)6 b(\264)-39
2227 b(edicat)21 b(unaire)h(qui)f(est)g(vrai)g(si)g(son)g(param)6
2228 b(\036)-39 b(etre)22 b(est)f(petit,)g Fj(entr)l(e)g Fp(le)h(pr)6
2229 b(\264)-39 b(edicat)-364 5268 y(ternaire)24 b(qui)e(est)h(vrai)g(si)g
2230 (son)f(premier)i(param)6 b(\036)-39 b(etre)23 b(est)g(entre)g(le)g
2231 (second)g(et)g(le)h(troisi)6 b(\036)-39 b(eme)22 b(et)h
2232 Fj(de)o(vant)h Fp(le)f(pr)6 b(\264)-39 b(edicat)23 b(unaire)g(qui)g
2233 (est)-364 5388 y(vrai)h(si)f(son)h(premier)f(param)6
2234 b(\036)-39 b(etre)25 b(est)e(de)n(v)n(ant)g(son)g(second)h(param)6
2235 b(\036)-39 b(etre.)24 b(Dans)f(la)h(formule)f(sui)n(v)n(ante)f(toutes)h
2236 (les)h(occurences)g(de)-364 5508 y(x)h(sont)f(li)6 b(\264)-39
2237 b(ees.)223 5724 y Fm(8)p Fl(x)17 b(:)g Fj(dodec)p Fi(\()p
2238 Fl(x)p Fi(\))23 b Fm(_)f Fl(dev)t(ant)p Fi(\()p Fl(x;)17
2239 b(y)t Fi(\))27 b Fm(\))h Fi(\(\()p Fm(9)p Fl(y)20 b(:)d(cube)p
2240 Fi(\()p Fl(y)t Fi(\))k Fm(^)h(:)p Fl(dev)t(ant)p Fi(\()p
2241 Fl(x;)17 b(y)t Fi(\)\))22 b Fm(^)h Fl(entr)s(e)p Fi(\()p
2242 Fl(u;)17 b(y)t(;)g(x)p Fi(\)\))-364 5939 y Fp(L)-9 b('assertion)24
2243 b(propos)6 b(\264)-39 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16
2244 b(?)-217 6059 y(Q.)23 b(29.)g(Soit)g Fl(p)p Fp(,)g Fl(q)t
2245 Fp(,)h Fl(r)i Fp(trois)c(v)n(ariables)h(propostionnelles.)e(L)-9
2246 b('ensemble)23 b Fm(f)p Fl(p)16 b Fm(^)h Fl(q)t Fm(g)24
2247 b Fp(a-t-il)f(pour)g(cons)6 b(\264)-39 b(equence)23 b(logique)g
2248 Fl(p)16 b Fm(_)i Fl(q)i Fp(?)-217 6180 y(Q.)k(30.)h Fn(\023)20
2249 b Fl(B)30 b Fp(est)24 b(une)h(condition)f(n)6 b(\264)-39
2250 b(ecessaire)25 b(pour)f Fl(A)c Fn(\024)25 b Fp(peut-elle)31
2251 b(\210)-39 b(etre)25 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39
2252 b(ee)26 b(par)f Fm(:)p Fl(B)33 b Fm(\))27 b(:)p Fl(A)18
2253 b Fp(?)1855 6429 y(3)p eop end
2255 TeXDict begin 4 3 bop -217 -264 a Fp(Q.)24 b(31.)h Fn(\023)20
2256 b Fl(B)30 b Fp(seulement)24 b(si)g Fl(A)c Fn(\024)25
2257 b Fp(peut-elle)30 b(\210)-38 b(etre)25 b(repr)6 b(\264)-39
2258 b(esent)6 b(\264)-39 b(ee)26 b(par)f Fm(:)p Fl(A)j Fm(\))f
2259 Fl(B)22 b Fp(?)-217 -144 y(Q.)28 b(32.)g(En)g(logique)f(des)i
2260 (propositions,)d Fl(P)42 b Fp(se)28 b(d)6 b(\264)-39
2261 b(eduit)28 b(syntaxiquement)e(de)j Fl(H)2592 -129 y Fk(1)2631
2262 -144 y Fp(,)f(.)15 b(.)g(.)g(,)28 b Fl(H)2938 -129 y
2263 Fh(n)3014 -144 y Fp(si)g(et)g(seulement)g(si)f Fl(P)42
2264 b Fp(est)29 b(une)-364 -23 y(cons)6 b(\264)-39 b(equence)25
2265 b(logique)f(de)h Fl(H)694 -8 y Fk(1)733 -23 y Fp(,)g(.)15
2266 b(.)g(.)g(,)24 b Fl(H)1033 -8 y Fh(n)1080 -23 y Fp(.)h(L)-9
2267 b('assertion)24 b(propos)6 b(\264)-39 b(ee)24 b(est)h(vraie)g(ou)g(f)o
2268 (ausse)16 b(?)-217 97 y(Q.)24 b(33.)h Fn(\023)20 b Fl(B)30
2269 b Fp(seulement)24 b(si)g Fl(A)c Fn(\024)25 b Fp(peut-elle)30
2270 b(\210)-38 b(etre)25 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39
2271 b(ee)26 b(par)f Fl(A)d Fm(_)g(:)p Fl(B)h Fp(?)-217 217
2272 y(Q.)h(34.)h(Soit)f(la)h(d)6 b(\264)-39 b(emonstration)23
2273 b(syntaxique)h(sui)n(v)n(ante)f(:)-314 332 y(D)6 b(\264)-39
2274 b(emonstration)-314 452 y(1.)99 b Fm(:)p Fl(B)34 b Fm(\))27
2275 b(:)p Fl(A)106 b(H)487 467 y Fk(1)-314 572 y Fp(2.)99
2276 b Fl(A)473 b(H)487 587 y Fk(2)-314 693 y Fp(3.)p -134
2277 693 30 4 v -98 693 V -62 693 V -26 693 V 10 693 V 412
2278 693 V 448 693 V 484 693 V 520 693 V 556 693 V -314 813
2279 a(4.)p -134 813 V -98 813 V -62 813 V -26 813 V 10 813
2280 V 412 813 V 448 813 V 484 813 V 520 813 V 556 813 V -314
2281 933 a(5.)99 b Fm(::)p Fl(B)340 b Fp(r)6 b(\264)-39 b(eduction)24
2282 b(de)h(l'absurde)g(entre)g(4.)g(et)f(1.)-314 1054 y(6.)99
2283 b Fm(::)p Fl(B)34 b Fm(\))27 b Fl(B)105 b Fp(Axiome)24
2284 b(9.)-314 1174 y(7.)99 b Fl(B)472 b Fp(mp)24 b(entre)h(5.)g(et)g(6.)
2285 1891 754 y(Si)f(elle)30 b(\264)-39 b(etait)24 b(compl)6
2286 b(\036)-39 b(ete)24 b(cela)g(permetrait)g(d)6 b(\264)-39
2287 b(emontrer)23 b(syntaxi-)-364 1287 y(quement)h(le)h(th)6
2288 b(\264)-39 b(eor)6 b(\036)-39 b(eme)25 b(de)g(la)f(contrapos)6
2289 b(\264)-39 b(ee.)25 b(Vrai)g(ou)g(f)o(aux)16 b(?)-217
2290 1407 y(Q.)24 b(35.)h(Soit)f Fl(p)p Fp(,)h Fl(q)t Fp(,)g
2291 Fl(r)i Fp(trois)d(v)n(ariables)g(propostionnelles.)f(La)i(relation)f
2292 Fm(f)p Fl(p)j Fm(\))h Fl(q)e Fm(_)c Fl(r)m(;)17 b Fm(:)p
2293 Fl(q)t Fm(g)28 b(j)-17 b Fi(=)28 b Fl(p)22 b Fm(_)g Fl(r)28
2294 b Fp(est-elle)c(vraie)17 b(?)-217 1509 y(Q.)24 b(36.)h(On)f(consid)6
2295 b(\036)-39 b(ere)25 b(la)g(base)g(de)g(connaissances)f(sui)n(v)n(ante)f
2296 (:)-364 1671 y Ff(parent\(pam,bob\).)-364 1750 y(parent\(tom,bob\).)
2297 -364 1829 y(parent\(tom,liz\).)-364 1908 y(parent\(bob,ann\).)-364
2298 1986 y(parent\(bob,pat\).)-364 2065 y(parent\(pat,jim\).)-364
2299 2223 y(ancetre\(X,Z\))38 b(:-)i(parent\(X,Z\).)-364 2302
2300 y(ancetre\(X,Z\))e(:-)i(parent\(X,Y\),ancetre\(Y,Z\).)-217
2301 2464 y Fp(On)24 b(soumet)g(la)h(requ)6 b(\210)-39 b(ete)25
2302 b(:)-364 2626 y Ff(?-)40 b(ancetre\(pam,X\).)-217 2829
2303 y Fp(Prolog)24 b(donne)h(4)f(r)6 b(\264)-39 b(eponses)25
2304 b(distinctes)e(et)30 b(\264)-38 b(echoue.)25 b(L)-9 b('assertion)24
2305 b(propos)6 b(\264)-39 b(ee)24 b(est)h(vraie)g(ou)g(f)o(ausse)16
2306 b(?)-217 2950 y(Q.)25 b(37.)f Fn(\023)c Fp(Il)26 b(est)e(f)o(aux)i(que)
2307 f(sa)g(m)6 b(\036)-39 b(ere)25 b(est)g(anglaise)g(ou)f(que)h(son)g(p)6
2308 b(\036)-39 b(ere)26 b(est)f(franc)-38 b(\270)5 b(ais)20
2309 b Fn(\024)25 b Fp(est-elle)31 b(\264)-39 b(equi)n(v)n(alente)29
2310 b(\036)-38 b(a)25 b Fn(\023)20 b Fp(sa)25 b(m)6 b(\036)-39
2311 b(ere)26 b(est)-364 3070 y(anglaise)f(ou)f(son)g(p)6
2312 b(\036)-39 b(ere)26 b(n'est)e(pas)h(franc)-38 b(\270)6
2313 b(ais)19 b Fn(\024)e Fp(?)-217 3190 y(Q.)34 b(38.)g(Soit)g
2314 Fl(p)p Fp(,)h Fl(q)t Fp(,)f Fl(r)j Fp(trois)d(v)n(ariables)g
2315 (propostionnelles.)e(L)-9 b(')6 b(\264)-39 b(enonc)6
2316 b(\264)-39 b(e)34 b(sui)n(v)n(ant)f(est-il)h(une)g(tautologie)15
2317 b(?)35 b Fi(\()p Fl(p)29 b Fm(_)h Fl(q)t Fi(\))f Fm(^)h
2318 Fl(r)48 b Fm(\()-364 3311 y Fi(\()p Fl(p)22 b Fm(_)h
2319 Fl(r)s Fi(\))f Fm(^)g Fi(\()p Fl(q)k Fm(_)d Fl(r)s Fi(\))p
2320 Fp(.)-217 3431 y(Q.)h(39.)h Fn(\023)20 b Fl(B)30 b Fp(seulement)24
2321 b(si)g Fl(A)c Fn(\024)25 b Fp(peut-elle)30 b(\210)-38
2322 b(etre)25 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39 b(ee)26
2323 b(par)f Fl(A)i Fm(\))h Fl(B)22 b Fp(?)-217 3551 y(Q.)i(40.)h
2324 Fn(\023)20 b Fl(A)30 b Fp(\036)-38 b(a)25 b(moins)f(que)g
2325 Fl(B)h Fn(\024)g Fp(peut-elle)30 b(\210)-38 b(etre)25
2326 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39 b(ee)26 b(par)f
2327 Fl(B)i Fm(_)c Fl(A)16 b Fp(?)-217 3672 y(Q.)22 b(41.)g(La)h(n)6
2328 b(\264)-39 b(egation)21 b(de)i Fn(\023)18 b Fp(ce)23
2329 b(triangle)f(est)g(rectangle)h(donc)f(ce)i(triangle)e(poss)6
2330 b(\036)-39 b(ede)22 b(un)g(angle)g(droit)c Fn(\024)k
2331 Fp(est-elle)h Fn(\023)18 b Fp(ce)23 b(triangle)-364 3792
2332 y(ne)i(poss)6 b(\036)-39 b(ede)24 b(pas)h(un)g(angle)f(droit)h(et)f
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2339 b(\036)-39 b(etre)21 b(est)h(un)f(cube,)g Fj(petit)i
2340 Fp(le)e(pr)6 b(\264)-39 b(edicat)21 b(unaire)h(qui)f(est)g(vrai)g(si)g
2341 (son)g(param)6 b(\036)-39 b(etre)22 b(est)f(petit,)g
2342 Fj(entr)l(e)g Fp(le)h(pr)6 b(\264)-39 b(edicat)-364 4153
2343 y(ternaire)24 b(qui)e(est)h(vrai)g(si)g(son)f(premier)i(param)6
2344 b(\036)-39 b(etre)23 b(est)g(entre)g(le)g(second)g(et)g(le)h(troisi)6
2345 b(\036)-39 b(eme)22 b(et)h Fj(de)o(vant)h Fp(le)f(pr)6
2346 b(\264)-39 b(edicat)23 b(unaire)g(qui)g(est)-364 4274
2347 y(vrai)i(si)f(son)h(premier)f(param)6 b(\036)-39 b(etre)26
2348 b(est)e(de)n(v)n(ant)g(son)g(second)h(param)6 b(\036)-39
2349 b(etre.)-217 4394 y(Les)24 b(formules)820 4514 y Fm(9)p
2350 Fl(x)17 b(:)g(dodec)p Fi(\()p Fl(x)p Fi(\))22 b Fm(^)g
2351 Fl(petit)p Fi(\()p Fl(x)p Fi(\))k Fp(et)f Fm(9)p Fl(x)17
2352 b(:)g(dodec)p Fi(\()p Fl(x)p Fi(\))28 b Fm(\))f Fl(petit)p
2353 Fi(\()p Fl(x)p Fi(\))-364 4689 y Fp(n'ont)d(jamais)g(la)h(m)6
2354 b(\210)-39 b(eme)25 b(v)n(aleur)f(de)h(v)6 b(\264)-39
2355 b(erit)6 b(\264)-39 b(e.)25 b(L)-9 b('assertion)24 b(propos)6
2356 b(\264)-39 b(ee)24 b(est)h(vraie)g(ou)f(f)o(ausse)17
2357 b(?)-217 4809 y(Q.)24 b(43.)h(Dans)f(la)h(formule)g Fl(P)14
2358 b Fi(\()p Fl(a)p Fi(\))27 b Fm(\))g Fl(Q)p Fi(\()p Fl(a)p
2359 Fi(\))e Fp(la)g(v)n(ariable)f Fl(a)i Fp(n'est)e(pas)h(li)6
2360 b(\264)-39 b(ee.)24 b(L)-9 b('assertion)24 b(propos)6
2361 b(\264)-39 b(ee)25 b(est)g(vraie)g(ou)f(f)o(ausse)17
2362 b(?)-217 4930 y(Q.)35 b(44.)g(Soit)g Fl(p)p Fp(,)h Fl(q)t
2363 Fp(,)f Fl(r)j Fp(trois)d(v)n(ariables)f(propostionnelles.)f(L)-9
2364 b('ensemble)35 b Fl(p)30 b Fm(^)g Fl(q)40 b Fp(est-elle)35
2365 b(une)g(cons)6 b(\264)-39 b(equence)36 b(logique)e(de)-364
2366 5050 y Fm(f)p Fl(p;)17 b(q)t Fm(g)f Fp(?)-217 5151 y(Q.)24
2367 b(45.)h(Dans)f(les)h(clauses)-364 5313 y Ff(pere_de\(Y,Z\))38
2368 b(:-)i(homme\(Y\),a_pour_fils\(Y,Z\).)-364 5392 y(pere_de\(Y,Z\))e(:-)i
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2370 b('ensemble)24 b(des)g(deux)h(clauses)g(se)f(traduit)g(en)156
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2376 Fl(y)t Fi(\))e Fm(^)i Fj(a)p 2943 5815 V 36 w(pour)p
2377 3168 5815 V 35 w(\002lle)o Fi(\()p Fl(y)t(;)17 b(z)t
2378 Fi(\)\))-364 6035 y Fp(L)-9 b('assertion)24 b(propos)6
2379 b(\264)-39 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16
2380 b(?)-217 6134 y(Q.)24 b(46.)h(On)f(consid)6 b(\036)-39
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2387 130 y(parent\(pat,jim\).)-217 332 y Fp(Au)24 b(requ)6
2388 b(\036)-39 b(etes)25 b(successi)n(v)o(es)e(:)-364 517
2389 y Ff(?-)40 b(parent\(jim,X\).)-364 596 y(?-)g(parent\(X,jim\).)-364
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2391 y(?-)i(parent\(pam,X\),)e(parent\(X,Y\),)g(parent\(Y,jim\).)-217
2392 980 y Fp(Prolog)24 b(r)6 b(\264)-39 b(epond)25 b(au)g(moins)e(deux)i
2393 (fois)f(f)o(aux)h(L)-9 b('assertion)24 b(propos)6 b(\264)-39
2394 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16 b(?)-217 1101
2395 y(Q.)33 b(47.)h(Soit)g Fl(a)g Fp(et)g Fl(b)h Fp(des)e(symboles)g(de)h
2396 (constante,)f Fl(f)45 b Fp(un)34 b(symbole)e(de)i(fonction)g(unaire,)g
2397 Fl(g)j Fp(un)d(symbole)e(de)i(fonction)-364 1221 y(binaire)25
2398 b(et)g Fl(S)30 b Fp(un)25 b(symbole)e(de)i(relation)g(binaire.)f(On)h
2399 (donne)f(les)h(e)o(xpressions)e(sui)n(v)n(antes)g(:)-243
2400 1377 y(1.)48 b Fl(g)t Fi(\()p Fl(a;)17 b(f)11 b Fi(\()p
2401 Fl(b)p Fi(\)\))-243 1533 y Fp(2.)48 b Fl(S)6 b Fi(\()p
2402 Fl(f)11 b Fi(\()p Fl(a)p Fi(\))p Fl(;)17 b(g)t Fi(\()p
2403 Fl(x;)g(f)11 b Fi(\()p Fl(y)t Fi(\)\)\))-217 1688 y Fp(L)-9
2404 b('e)o(xpression)23 b(2)i(est)f(un)h(terme)g(comple)o(x)o(e.)e(L)-9
2405 b('assertion)24 b(propos)6 b(\264)-39 b(ee)24 b(est)h(vraie)g(ou)f(f)o
2406 (ausse)17 b(?)-217 1809 y(Q.)j(48.)f(Une)h(base)h(de)f(connaissance)f
2407 (Prolog)h(est)g(un)g(ensemble)f(de)h(f)o(aits,)g(de)g(r)6
2408 b(\036)-39 b(egles)20 b(et)g(de)h(requ)6 b(\210)-39 b(etes.)20
2409 b(L)-9 b('assertion)19 b(propos)6 b(\264)-39 b(ee)-364
2410 1929 y(est)25 b(vraie)g(ou)f(f)o(ausse)17 b(?)-217 2049
2411 y(Q.)39 b(49.)h(On)f(consid)6 b(\036)-39 b(ere)40 b(les)f(pr)6
2412 b(\264)-39 b(edicats)40 b(et)f(constantes)g(sui)n(v)n(ants)f(a)n(v)o
2413 (ec)h(leur)h(interpr)6 b(\264)-39 b(etation)39 b(sur)g(un)h(uni)n(v)o
2414 (ers)e(constitu)6 b(\264)-39 b(e)-364 2170 y(d'indi)n(vidus)23
2415 b(humains.)p 1172 2287 1417 4 v 1172 2406 4 121 v 1402
2416 2370 a(pr)6 b(\264)-39 b(edicat)p 1772 2406 V 103 w(sens)p
2417 2585 2406 V 1172 2408 1417 4 v 1172 2526 4 121 v 1303
2418 2490 a Fj(aime)o Fi(\()p Fl(x;)17 b(y)t Fi(\))p 1772
2419 2526 V 103 w Fl(x)25 b Fp(aime)f Fl(y)p 2585 2526 V 1172
2420 2647 V 1225 2611 a Fj(maries)o Fi(\()p Fl(x;)17 b(y)t
2421 Fi(\))p 1772 2647 V 103 w Fl(x)25 b Fp(et)g Fl(y)j Fp(sont)c(mari)6
2422 b(\264)-39 b(es)p 2585 2647 V 1172 2767 V 1331 2731 a
2423 Fj(femme)p Fi(\()p Fl(x)p Fi(\))p 1772 2767 V 104 w Fl(x)25
2424 b Fp(est)f(une)h(femme)p 2585 2767 V 1172 2888 V 1304
2425 2851 a Fj(homme)o Fi(\()p Fl(x)p Fi(\))p 1772 2888 V
2426 104 w Fl(x)g Fp(est)f(un)h(homme)p 2585 2888 V 1172 3008
2427 V 1376 2972 a Fj(\002dele)o Fi(\()p Fl(x)p Fi(\))p 1772
2428 3008 V 104 w Fl(x)g Fp(est)f(\002d)6 b(\036)-39 b(ele)p
2429 2585 3008 V 1172 3128 V 1326 3092 a Fj(honete)o Fi(\()p
2430 Fl(x)p Fi(\))p 1772 3128 V 104 w Fl(x)25 b Fp(dit)f(la)h(v)6
2431 b(\264)-39 b(erit)6 b(\264)-39 b(e)p 2585 3128 V 1172
2432 3249 V 1671 3213 a Fl(a)p 1772 3249 V 104 w Fp(Alice)p
2433 2585 3249 V 1172 3369 V 1681 3333 a Fl(b)p 1772 3369
2434 V 104 w Fp(Bob)p 2585 3369 V 1172 3489 V 1681 3453 a
2435 Fl(c)p 1772 3489 V 103 w Fp(Clinton)p 2585 3489 V 1172
2436 3491 1417 4 v 1018 3724 a Fm(8)p Fl(x)17 b(:)g Fj(femme)p
2437 Fi(\()p Fl(x)p Fi(\))28 b Fm(\))f Fi(\()p Fj(aime)p Fi(\()p
2438 Fl(x;)17 b(b)p Fi(\))23 b Fm(_)f Fj(aime)p Fi(\()p Fl(x;)17
2439 b(c)p Fi(\)\))-217 3898 y Fp(peut)24 b(se)h(traduire)g(en)g
2440 Fn(\023)20 b Fp(Si)25 b(une)f(femme)h(n'aime)g(pas)f(Clinton,)g(alors)h
2441 (elle)f(aime)h(Bob)20 b Fn(\024)p Fp(.)-217 4018 y(L)-9
2442 b('assertion)23 b(propos)6 b(\264)-39 b(ee)25 b(est)g(vraie)g(ou)f(f)o
2443 (ausse)17 b(?)-217 4139 y(Q.)33 b(50.)h(Soit)g Fl(a)g
2444 Fp(et)g Fl(b)h Fp(des)e(symboles)g(de)h(constante,)f
2445 Fl(f)45 b Fp(un)34 b(symbole)e(de)i(fonction)g(unaire,)g
2446 Fl(g)j Fp(un)d(symbole)e(de)i(fonction)-364 4259 y(binaire)25
2447 b(et)g Fl(S)30 b Fp(un)25 b(symbole)e(de)i(relation)g(binaire.)f(On)h
2448 (donne)f(les)h(e)o(xpressions)e(sui)n(v)n(antes)g(:)-243
2449 4415 y(1.)48 b Fl(g)t Fi(\()p Fl(a;)17 b(f)11 b Fi(\()p
2450 Fl(b)p Fi(\)\))-243 4571 y Fp(2.)48 b Fl(S)6 b Fi(\()p
2451 Fl(f)11 b Fi(\()p Fl(a)p Fi(\))p Fl(;)17 b(g)t Fi(\()p
2452 Fl(x;)g(f)11 b Fi(\()p Fl(y)t Fi(\)\)\))-217 4726 y Fp(L)-9
2453 b('e)o(xpression)23 b(1)i(contient)f(quatre)g(termes)h(L)-9
2454 b('assertion)24 b(propos)6 b(\264)-39 b(ee)24 b(est)h(vraie)g(ou)g(f)o
2455 (ausse)16 b(?)-217 4847 y(Q.)24 b(51.)h(Soit)f Fl(f)11
2456 b Fp(,)25 b Fl(g)j Fp(des)d(symboles)e(de)i(fonctions)f(binaire,)g
2457 Fl(R)i Fp(un)f(symbole)e(de)i(relation)f(binaire.)h(Soit)f
2458 Fl(A)h Fp(la)g(formule)834 5065 y Fi(\()p Fm(8)p Fl(z)c(:)c(R)q
2459 Fi(\()p Fl(x;)g(z)t Fi(\))23 b Fm(^)g Fl(R)q Fi(\()p
2460 Fl(z)t(;)17 b(y)t Fi(\)\))27 b Fm(\))g Fi(\()p Fm(9)p
2461 Fl(z)22 b(:)17 b(R)q Fi(\()p Fl(z)t(;)g(y)t Fi(\))k Fm(_)i
2462 Fl(R)q Fi(\()p Fl(x;)17 b(z)t Fi(\)\))g Fl(:)-364 5284
2463 y Fp(Soit)25 b Fl(u)p Fp(,)f Fl(v)29 b Fp(les)24 b(termes)h(d)6
2464 b(\264)-39 b(e\002nis)24 b(par)i Fl(u)h Fi(=)g Fl(f)11
2465 b Fi(\()p Fl(z)t(;)17 b(x)p Fi(\))26 b Fp(et)e Fl(v)32
2466 b Fi(=)27 b Fl(g)t Fi(\()p Fl(x;)17 b(z)t Fi(\))-217
2467 5404 y Fp(Alors)24 b(on)g(a)1165 5524 y Fl(A)p Fi(\()p
2468 Fl(u=x)p Fi(\)\()p Fl(v)t(=y)t Fi(\))i Fm(\021)i Fl(A)p
2469 Fi(\()p Fl(v)t(=y)t Fi(\)\()p Fl(u)p Fi(\()p Fl(v)t(=y)t
2470 Fi(\))p Fl(=x)p Fi(\))-364 5698 y Fp(L)-9 b('assertion)24
2471 b(propos)6 b(\264)-39 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16
2472 b(?)-217 5818 y(Q.)24 b(52.)h(Si)f(je)h(tra)n(v)n(aille,)f(je)h(ne)g
2473 (peux)f(pas)30 b(\264)-38 b(etudier)16 b(;)25 b(Soit)f(je)h(tra)n(v)n
2474 (aille,)e(soit)h(je)h(suis)f(rec)-38 b(\270)5 b(u)25
2475 b(en)g(math)6 b(\264)-39 b(ematiques)15 b(;)24 b(j'ai)30
2476 b(\264)-38 b(et)6 b(\264)-39 b(e)25 b(rec)-38 b(\270)6
2477 b(u)-364 5939 y(en)25 b(math)6 b(\264)-39 b(ematiques.)23
2478 b(Donc)i(j'ai)30 b(\264)-38 b(etudi)6 b(\264)-39 b(e.)24
2479 b(Le)h(raisonnement)f(propos)6 b(\264)-39 b(e)24 b(est-il)g(incorrect)
2480 17 b(?)-217 6059 y(Q.)29 b(53.)g(Soit)h Fj(dodec)f Fp(le)h(pr)6
2481 b(\264)-39 b(edicat)30 b(unaire)g(qui)f(est)g(vrai)h(si)f(son)g(param)6
2482 b(\036)-39 b(etre)30 b(est)g(un)f(dod)6 b(\264)-39 b(eca)6
2483 b(\036)-39 b(edre,)30 b Fj(cube)g Fp(le)g(pr)6 b(\264)-39
2484 b(edicat)29 b(unaire)-364 6180 y(qui)h(est)g(vrai)g(si)g(son)f(param)6
2485 b(\036)-39 b(etre)31 b(est)f(un)g(cube,)g Fj(petit)h
2486 Fp(le)g(pr)6 b(\264)-39 b(edicat)30 b(unaire)g(qui)g(est)g(vrai)g(si)g
2487 (son)f(param)6 b(\036)-39 b(etre)31 b(est)f(petit,)f
2488 Fj(entr)l(e)h Fp(le)1855 6429 y(5)p eop end
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2889 @endspecial 1096 1548 a Fp(F)t Fd(I)t(G)t Fp(.)30 b(1)25
2890 b(\226)f(Graphe)31 b(\036)-39 b(a)26 b(mod)6 b(\264)-39
2891 b(eliser)23 b(en)i(Prolog)-364 1835 y(pr)6 b(\264)-39
2892 b(edicat)35 b(ternaire)f(qui)g(est)g(vrai)g(si)g(son)g(premier)g(param)
2893 6 b(\036)-39 b(etre)35 b(est)f(entre)g(le)h(second)f(et)g(le)g(troisi)6
2894 b(\036)-39 b(eme)34 b(et)g Fj(de)o(vant)h Fp(le)g(pr)6
2895 b(\264)-39 b(edicat)-364 1956 y(unaire)25 b(qui)f(est)h(vrai)g(si)f
2896 (son)h(premier)f(param)6 b(\036)-39 b(etre)26 b(est)e(de)n(v)n(ant)g
2897 (son)g(second)h(param)6 b(\036)-39 b(etre.)25 b(Dans)f(la)h(formule)g
2898 (sui)n(v)n(ante)e Fl(y)28 b Fp(et)d Fl(u)f Fp(ont)-364
2899 2076 y(des)h(occurences)g(libres)223 2296 y Fm(8)p Fl(x)17
2900 b(:)g Fj(dodec)p Fi(\()p Fl(x)p Fi(\))23 b Fm(_)f Fl(dev)t(ant)p
2901 Fi(\()p Fl(x;)17 b(y)t Fi(\))27 b Fm(\))h Fi(\(\()p Fm(9)p
2902 Fl(y)20 b(:)d(cube)p Fi(\()p Fl(y)t Fi(\))k Fm(^)h(:)p
2903 Fl(dev)t(ant)p Fi(\()p Fl(x;)17 b(y)t Fi(\)\))22 b Fm(^)h
2904 Fl(entr)s(e)p Fi(\()p Fl(u;)17 b(y)t(;)g(x)p Fi(\)\))-364
2905 2516 y Fp(L)-9 b('assertion)24 b(propos)6 b(\264)-39
2906 b(ee)25 b(est)f(vraie)h(ou)g(f)o(ausse)16 b(?)-217 2636
2907 y(Q.)24 b(54.)h Fn(\023)20 b Fl(A)30 b Fp(\036)-38 b(a)25
2908 b(moins)f(que)g Fl(B)h Fn(\024)g Fp(peut-elle)30 b(\210)-38
2909 b(etre)25 b(repr)6 b(\264)-39 b(esent)6 b(\264)-39 b(ee)26
2910 b(par)f Fl(B)33 b Fm(\))27 b Fl(A)17 b Fp(?)-217 2757
2911 y(Q.)24 b(55.)h(L)-9 b('af)n(\002rmation)24 b Fn(\023)c
2912 Fp(le)25 b(V)-11 b(esuv)o(e)24 b(ferra)i(une)f(irruption)e(en)i(2010)19
2913 b Fn(\024)25 b Fp(est-elle)g(une)g(proposition)14 b(?)-217
2914 2877 y(Q.)27 b(56.)h Fn(\023)21 b Fp(Il)28 b(est)g(f)o(aux)g(qu'il)f
2915 (ne)h(f)o(ait)g(pas)f(froid)h(ou)g(qu'il)f(pleut)20 b
2916 Fn(\024)28 b Fp(est-elle)34 b(\264)-39 b(equi)n(v)n(alente)32
2917 b(\036)-39 b(a)29 b Fn(\023)21 b Fp(il)27 b(f)o(ait)h(froid)g(mais)f
2918 (il)g(ne)h(pleut)-364 2998 y(pas)20 b Fn(\024)d Fp(?)-364
2919 3337 y Fo(2)143 b(Raisonnements)828 3335 y(\264)820 3337
2920 y(ecrits)34 b(\(1h15\))-364 3590 y Fc(2.1)119 b(Calcul)31
2921 b(des)f(pr)589 3589 y(\264)582 3590 y(edicats)-217 3777
2922 y Fp(Dans)i(la)h(s)6 b(\264)-39 b(erie)33 b(sui)n(v)n(ante,)d(chaque)j
2923 (formule)f(est)h(logiquement)j(\264)-38 b(equi)n(v)n(alente)36
2924 b(\036)-38 b(a)33 b(une)f(et)h(une)g(seule)f(autre.)h(Retrouv)o(er)g
2925 (les)-364 3898 y(paires)e(\264)-39 b(equi)n(v)n(alentes)23
2926 b(et)i(justi\002er)-5 b(.)1527 4118 y Fm(8)p Fl(x)17
2927 b(:)g Fm(:)p Fl(p)p Fi(\()p Fl(x)p Fi(\))23 b Fm(^)f
2928 Fl(q)t Fi(\()p Fl(x)p Fi(\))1775 b Fp(\(1\))1467 4263
2929 y Fm(:)p Fi(\()p Fm(8)p Fl(x)17 b(:)g(p)p Fi(\()p Fl(x)p
2930 Fi(\))28 b Fm(\))g Fl(q)t Fi(\()p Fl(x)p Fi(\)\))1714
2931 b Fp(\(2\))1494 4408 y Fm(9)p Fl(x)17 b(:)g Fm(:)p Fl(p)p
2932 Fi(\()p Fl(x)p Fi(\))23 b Fm(_)f(:)p Fl(q)t Fi(\()p Fl(x)p
2933 Fi(\))1742 b Fp(\(3\))1527 4554 y Fm(9)p Fl(x)17 b(:)g
2934 Fm(:)p Fl(p)p Fi(\()p Fl(x)p Fi(\))23 b Fm(_)f Fl(q)t
2935 Fi(\()p Fl(x)p Fi(\))1775 b Fp(\(4\))1366 4699 y Fi(\()p
2936 Fm(9)p Fl(x)17 b(:)g Fm(:)p Fl(p)p Fi(\()p Fl(x)p Fi(\)\))22
2937 b Fm(_)h Fi(\()p Fm(9)p Fl(x)17 b(:)g(q)t Fi(\()p Fl(x)p
2938 Fi(\)\))1613 b Fp(\(5\))1299 4844 y Fi(\()p Fm(9)p Fl(x)17
2939 b(:)g Fm(:)p Fl(p)p Fi(\()p Fl(x)p Fi(\)\))23 b Fm(_)g(:)p
2940 Fi(\()p Fm(9)p Fl(x)17 b(:)g Fm(:)p Fl(q)t Fi(\()p Fl(x)p
2941 Fi(\)\))1547 b Fp(\(6\))1366 4989 y Fm(:)p Fi(\()p Fm(9)p
2942 Fl(x)17 b(:)g(p)p Fi(\()p Fl(x)p Fi(\)\))22 b Fm(^)h
2943 Fi(\()p Fm(8)p Fl(x)17 b(:)g(q)t Fi(\()p Fl(x)p Fi(\)\))1613
2944 b Fp(\(7\))1505 5135 y Fm(9)p Fl(x)17 b(:)g(p)p Fi(\()p
2945 Fl(x)p Fi(\))28 b Fm(\))f(:)p Fl(q)t Fi(\()p Fl(x)p Fi(\))1753
2946 b Fp(\(8\))1366 5280 y Fm(:)p Fi(\()p Fm(8)p Fl(x)17
2947 b(:)g(p)p Fi(\()p Fl(x)p Fi(\)\))22 b Fm(_)h Fi(\()p
2948 Fm(8)p Fl(x)17 b(:)g(q)t Fi(\()p Fl(x)p Fi(\)\))1613
2949 b Fp(\(9\))1527 5425 y Fm(9)p Fl(x)17 b(:)g(p)p Fi(\()p
2950 Fl(x)p Fi(\))23 b Fm(^)f(:)p Fl(q)t Fi(\()p Fl(x)p Fi(\))1725
2951 b Fp(\(10\))-364 5721 y Fc(2.2)119 b(Pr)n(olog)-364 5908
2952 y Fb(2.2.1)99 b(Graphe)-217 6096 y Fp(On)24 b(consid)6
2953 b(\036)-39 b(ere)25 b(le)g(graphe)g(donn)6 b(\264)-39
2954 b(e)30 b(\036)-39 b(a)25 b(la)g(\002gure)g(1.)1855 6429
2957 TeXDict begin 7 6 bop -243 -264 a Fp(1.)48 b(Mod)6 b(\264)-39
2958 b(eliser)24 b(ce)i(graphe)31 b(\036)-39 b(a)26 b(l'aide)f(du)g(pr)6
2959 b(\264)-39 b(edicat)25 b Fj(ar)l(c)p Fi(\()p Fl(X)r(;)17
2960 b(Y)22 b Fi(\))j Fp(qui)f(est)h(vrai)h(s'il)e(e)o(xiste)g(un)h(arc)h
2961 (depuis)f(le)g(noeud)g Fl(X)33 b Fp(v)o(ers)24 b(le)-120
2962 -144 y(noeud)g Fl(Y)e Fp(.)-243 12 y(2.)48 b(Construire)33
2963 b(le)g(pr)6 b(\264)-39 b(edicat)32 b Fj(c)o(hemin)p Fi(\()p
2964 Fl(X)r(;)17 b(Y)k Fi(\))33 b Fp(qui)f(est)h(vrai)g(s'il)f(e)o(xiste)g
2965 (un)g(chemin,)g(c'est)39 b(\036)-39 b(a)34 b(dire)e(une)h(suite)f
2966 (continue)g(et)-114 133 y(\264)-39 b(ev)o(entuellement)23
2967 b(vide)i(d'arcs)g(entre)g(les)g(noeuds)f Fl(X)32 b Fp(et)25
2968 b Fl(Y)46 b Fp(du)25 b(graphe.)-243 289 y(3.)48 b(Quelle)25
2969 b(requ)6 b(\210)-39 b(ete)25 b(Prolog)f(ef)n(fectueriez-v)n(ous)h(pour)
2970 g(obtenir)f(tous)g(les)g(noeuds)h(accessibles)30 b(\036)-39
2971 b(a)25 b(partir)g(du)g(noeud)f(a.)-364 555 y Fb(2.2.2)99
2972 b(Liste)25 b(d'entiers)i(natur)n(els)-243 743 y Fp(1.)48
2973 b(D)6 b(\264)-39 b(e\002nir)25 b(un)g(pr)6 b(\264)-39
2974 b(edicat)25 b Fj(pair)o Fi(\()p Fl(X)8 b Fi(\))24 b Fp(qui)g(est)h
2975 (vrai)g(si)f Fl(X)33 b Fp(est)25 b(un)f(nombre)g(pair)-5
2976 b(.)-243 899 y(2.)48 b(D)6 b(\264)-39 b(e\002nir)28 b(un)g(pr)6
2977 b(\264)-39 b(edicat)28 b Fj(membr)l(es)p 1029 899 30
2978 4 v 36 w(pair)o(s)o Fi(\()p Fl(L;)17 b(Lp)p Fi(\))28
2979 b Fp(qui)f(est)h(vrai)g(si)f(la)h(liste)f Fl(Lp)i Fp(est)e(compos)6
2980 b(\264)-39 b(ee)28 b(des)33 b(\264)-38 b(el)6 b(\264)-39
2981 b(ements)27 b(pairs)g(de)h(la)-120 1019 y(liste)c Fl(L)h
2982 Fp(et)g(dans)g(le)g(m)6 b(\210)-39 b(eme)24 b(ordre.)-243
2983 1176 y(3.)48 b(On)24 b(consid)6 b(\036)-39 b(ere)23 b(le)h(pr)6
2984 b(\264)-39 b(edicat)24 b(Prolog)g Fj(append)o Fi(\()p
2985 Fl(L)p Fi(1)p Fl(;)17 b(L)p Fi(2)p Fl(;)g(L)p Fi(3\))24
2986 b Fp(qui)f(est)g(est)h(vrai)g(si)f Fl(L)p Fi(3)h Fp(est)g(la)g(concat)6
2987 b(\264)-39 b(enation)23 b(des)h(listes)e Fl(L)p Fi(1)-120
2988 1296 y Fp(et)j Fl(L)p Fi(2)p Fp(.)g(D)6 b(\264)-39 b(e\002nir)25
2989 b(le)g(pr)6 b(\264)-39 b(edicat)25 b Fj(in)l(ver)o(se)o
2990 Fi(\()p Fl(L;)17 b(Lp)p Fi(\))26 b Fp(qui)e(est)g(vrai)h(si)g
2991 Fl(Lp)g Fp(est)f(la)h(liste)f Fl(L)h Fp(retourn)6 b(\264)-39
2992 b(ee.)-364 1591 y Fc(2.3)119 b(D)-2 1590 y(\264)-9 1591
2993 y(eduction)32 b(syntaxique)-217 1779 y Fp(Dans)24 b(ce)i(qui)e(suit,)g
2994 Fl(A)p Fp(,)g Fl(B)5 b Fp(,)25 b Fl(C)32 b Fp(et)25 b
2995 Fl(D)j Fp(sont)c(quatre)h(v)n(ariables)f(propositionnelles.)-243
2996 1953 y(1.)48 b(D)6 b(\264)-39 b(emontrer)25 b(le)f(th)6
2997 b(\264)-39 b(eor)6 b(\036)-39 b(eme)25 b(sui)n(v)n(ant)e(par)i(d)6
2998 b(\264)-39 b(eduction)24 b(syntaxique)f(:)1164 2173 y
2999 Fi(\()p Fl(A)28 b Fm(\))f Fi(\()p Fl(B)g Fm(^)c Fl(C)7
3000 b Fi(\)\))27 b Fm(\))h Fi(\()p Fl(A)f Fm(\))h Fl(B)5
3001 b Fi(\))22 b Fm(^)g Fi(\()p Fl(A)28 b Fm(\))g Fl(C)7
3002 b Fi(\))-120 2393 y Fp(On)25 b(pourra)g(utiliser)e(le)i(th)6
3003 b(\264)-39 b(eor)6 b(\036)-39 b(eme)25 b(de)g(transiti)n(vit)6
3004 b(\264)-39 b(e)22 b(de)j(l'implication.)-243 2549 y(2.)48
3005 b(Ef)n(fectuer)25 b(la)g(d)6 b(\264)-39 b(emonstration)23
3006 b(sous)h(hypoth)6 b(\036)-39 b(ese)23 b(sui)n(v)n(ante)g(:)1089
3007 2769 y Fm(f)p Fl(C)34 b Fm(\))28 b(:)p Fl(B)5 b(;)17
3008 b(C)29 b Fm(_)22 b Fl(D)s(;)17 b(D)30 b Fm(\))e(:)p Fl(B)5
3009 b(;)17 b(A)28 b Fm(\))f Fl(B)5 b Fm(g)28 b(`)f(:)p Fl(A)-120
3010 2989 y Fp(On)e(pourra)g(utiliser)e(le)i(th)6 b(\264)-39
3011 b(eor)6 b(\036)-39 b(eme)25 b(de)g(la)g(contrapos)6 b(\264)-39
3012 b(ee)24 b(et)h(la)g(r)6 b(\036)-39 b(egle)25 b(de)g(disjonction)e(des)h
3013 (cas.)1855 6429 y(7)p eop end
3015 TeXDict begin 8 7 bop -364 -260 a Fo(R)-252 -262 y(\264)-260
3016 -260 y(eponses)34 b(au)h(QCM)-364 -36 y Fp(Nom)24 b
3017 (:............................)-364 84 y(Pr)6 b(\264)-39
3018 b(enom)25 b(:............................)p -16 322 3793
3019 4 v -16 570 4 250 v 37 495 a Fa(Num)461 494 y(\264)450
3020 495 y(ero)p 764 570 V 103 w(V)p 1016 570 V 103 w(F)p
3021 1234 570 V 1255 570 V 123 w(Num)1731 494 y(\264)1720
3022 495 y(ero)p 2034 570 V 103 w(V)p 2286 570 V 103 w(F)p
3023 2504 570 V 2525 570 V 123 w(Num)3001 494 y(\264)2990
3024 495 y(ero)p 3303 570 V 102 w(V)p 3555 570 V 103 w(F)p
3025 3773 570 V -16 571 3793 4 v -16 819 4 250 v 37 744 a(Q.)52
3026 b(1)p 764 819 V 1016 819 V 1234 819 V 1255 819 V 914
3027 w(Q.)f(2)p 2034 819 V 2286 819 V 2504 819 V 2525 819
3028 V 915 w(Q.)g(3)p 3303 819 V 3555 819 V 3773 819 V -16
3029 821 3793 4 v -16 1068 4 250 v 37 993 a(Q.)h(4)p 764 1068
3030 V 1016 1068 V 1234 1068 V 1255 1068 V 914 w(Q.)f(5)p
3031 2034 1068 V 2286 1068 V 2504 1068 V 2525 1068 V 915 w(Q.)g(6)p
3032 3303 1068 V 3555 1068 V 3773 1068 V -16 1070 3793 4 v
3033 -16 1317 4 250 v 37 1242 a(Q.)h(7)p 764 1317 V 1016 1317
3034 V 1234 1317 V 1255 1317 V 914 w(Q.)f(8)p 2034 1317 V
3035 2286 1317 V 2504 1317 V 2525 1317 V 915 w(Q.)g(9)p 3303
3036 1317 V 3555 1317 V 3773 1317 V -16 1319 3793 4 v -16
3037 1566 4 250 v 37 1491 a(Q.)h(10)p 764 1566 V 1016 1566
3038 V 1234 1566 V 1255 1566 V 811 w(Q.)f(11)p 2034 1566 V
3039 2286 1566 V 2504 1566 V 2525 1566 V 812 w(Q.)g(12)p 3303
3040 1566 V 3555 1566 V 3773 1566 V -16 1568 3793 4 v -16
3041 1815 4 250 v 37 1740 a(Q.)h(13)p 764 1815 V 1016 1815
3042 V 1234 1815 V 1255 1815 V 811 w(Q.)f(14)p 2034 1815 V
3043 2286 1815 V 2504 1815 V 2525 1815 V 812 w(Q.)g(15)p 3303
3044 1815 V 3555 1815 V 3773 1815 V -16 1817 3793 4 v -16
3045 2064 4 250 v 37 1989 a(Q.)h(16)p 764 2064 V 1016 2064
3046 V 1234 2064 V 1255 2064 V 811 w(Q.)f(17)p 2034 2064 V
3047 2286 2064 V 2504 2064 V 2525 2064 V 812 w(Q.)g(18)p 3303
3048 2064 V 3555 2064 V 3773 2064 V -16 2066 3793 4 v -16
3049 2313 4 250 v 37 2239 a(Q.)h(19)p 764 2313 V 1016 2313
3050 V 1234 2313 V 1255 2313 V 811 w(Q.)f(20)p 2034 2313 V
3051 2286 2313 V 2504 2313 V 2525 2313 V 812 w(Q.)g(21)p 3303
3052 2313 V 3555 2313 V 3773 2313 V -16 2315 3793 4 v -16
3053 2562 4 250 v 37 2488 a(Q.)h(22)p 764 2562 V 1016 2562
3054 V 1234 2562 V 1255 2562 V 811 w(Q.)f(23)p 2034 2562 V
3055 2286 2562 V 2504 2562 V 2525 2562 V 812 w(Q.)g(24)p 3303
3056 2562 V 3555 2562 V 3773 2562 V -16 2564 3793 4 v -16
3057 2811 4 250 v 37 2737 a(Q.)h(25)p 764 2811 V 1016 2811
3058 V 1234 2811 V 1255 2811 V 811 w(Q.)f(26)p 2034 2811 V
3059 2286 2811 V 2504 2811 V 2525 2811 V 812 w(Q.)g(27)p 3303
3060 2811 V 3555 2811 V 3773 2811 V -16 2813 3793 4 v -16
3061 3060 4 250 v 37 2986 a(Q.)h(28)p 764 3060 V 1016 3060
3062 V 1234 3060 V 1255 3060 V 811 w(Q.)f(29)p 2034 3060 V
3063 2286 3060 V 2504 3060 V 2525 3060 V 812 w(Q.)g(30)p 3303
3064 3060 V 3555 3060 V 3773 3060 V -16 3062 3793 4 v -16
3065 3310 4 250 v 37 3235 a(Q.)h(31)p 764 3310 V 1016 3310
3066 V 1234 3310 V 1255 3310 V 811 w(Q.)f(32)p 2034 3310 V
3067 2286 3310 V 2504 3310 V 2525 3310 V 812 w(Q.)g(33)p 3303
3068 3310 V 3555 3310 V 3773 3310 V -16 3311 3793 4 v -16
3069 3559 4 250 v 37 3484 a(Q.)h(34)p 764 3559 V 1016 3559
3070 V 1234 3559 V 1255 3559 V 811 w(Q.)f(35)p 2034 3559 V
3071 2286 3559 V 2504 3559 V 2525 3559 V 812 w(Q.)g(36)p 3303
3072 3559 V 3555 3559 V 3773 3559 V -16 3560 3793 4 v -16
3073 3808 4 250 v 37 3733 a(Q.)h(37)p 764 3808 V 1016 3808
3074 V 1234 3808 V 1255 3808 V 811 w(Q.)f(38)p 2034 3808 V
3075 2286 3808 V 2504 3808 V 2525 3808 V 812 w(Q.)g(39)p 3303
3076 3808 V 3555 3808 V 3773 3808 V -16 3809 3793 4 v -16
3077 4057 4 250 v 37 3982 a(Q.)h(40)p 764 4057 V 1016 4057
3078 V 1234 4057 V 1255 4057 V 811 w(Q.)f(41)p 2034 4057 V
3079 2286 4057 V 2504 4057 V 2525 4057 V 812 w(Q.)g(42)p 3303
3080 4057 V 3555 4057 V 3773 4057 V -16 4058 3793 4 v -16
3081 4306 4 250 v 37 4231 a(Q.)h(43)p 764 4306 V 1016 4306
3082 V 1234 4306 V 1255 4306 V 811 w(Q.)f(44)p 2034 4306 V
3083 2286 4306 V 2504 4306 V 2525 4306 V 812 w(Q.)g(45)p 3303
3084 4306 V 3555 4306 V 3773 4306 V -16 4307 3793 4 v -16
3085 4555 4 250 v 37 4480 a(Q.)h(46)p 764 4555 V 1016 4555
3086 V 1234 4555 V 1255 4555 V 811 w(Q.)f(47)p 2034 4555 V
3087 2286 4555 V 2504 4555 V 2525 4555 V 812 w(Q.)g(48)p 3303
3088 4555 V 3555 4555 V 3773 4555 V -16 4557 3793 4 v -16
3089 4804 4 250 v 37 4729 a(Q.)h(49)p 764 4804 V 1016 4804
3090 V 1234 4804 V 1255 4804 V 811 w(Q.)f(50)p 2034 4804 V
3091 2286 4804 V 2504 4804 V 2525 4804 V 812 w(Q.)g(51)p 3303
3092 4804 V 3555 4804 V 3773 4804 V -16 4806 3793 4 v -16
3093 5053 4 250 v 37 4978 a(Q.)h(52)p 764 5053 V 1016 5053
3094 V 1234 5053 V 1255 5053 V 811 w(Q.)f(53)p 2034 5053 V
3095 2286 5053 V 2504 5053 V 2525 5053 V 812 w(Q.)g(54)p 3303
3096 5053 V 3555 5053 V 3773 5053 V -16 5055 3793 4 v -16
3097 5302 4 250 v 37 5227 a(Q.)h(55)p 764 5302 V 1016 5302
3098 V 1234 5302 V 1255 5302 V 811 w(Q.)f(56)p 2034 5302 V
3099 2286 5302 V 2504 5302 V 2525 5302 V 3303 5302 V 3555
3100 5302 V 3773 5302 V -16 5304 3793 4 v 1855 6429 a Fp(8)p
3104 userdict /end-hook known{end-hook}if
