EXAMEN FINAL 2020-3 - Discreta - Con El Profe Malorevisión Del Intento

 

5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Dfhnlzgkf nb

[unskgy, 5 kn Kndnhcnr kn 3939, 95=9?

Nstgkf @jlgbjzgkf @jlgbjzgkf nl

[unskgy, 5 kn Kndnhcnr kn 3939, 9:=4:

[jnhpf 7 efrg 43 hjlutfs nhpbngkf Dgbj`jdgdjôl Tjl dgbj`jdgr gýl Yrnoultg 7

Tngl bfs dflmultfs

Dfrrndtg Yultýg 7 sfcrn 7

Bg `uldjôl

ns knb tjpf=

Tnbnddjfln ulg= g. Tfcrnyndtjvg  c. Cjyndtjvg d. Dflstgltn k. Jlyndtjvg

Bg rnspunstg dfrrndtg ns= Tfcrnyndtjvg

Yrnoultg 3

^lg prfpfsjdjôl nqujvgbnltn g ~ Q(p \ q)

®

 rX,, ns6  rX

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. (p \ q) \ ~ r



c. ~ (p \ q) v ~r d. r \ (p \ q) k. (~p \ q) v r

Bg rnspunstg dfrrndtg ns= (p \ q) \ ~ r

Yrnoultg 4

Bg dfltrgpfsjtjvg kn bg dflkjdjflgb= ‒Tj vfy gb trgcgmf f gpruncf Kjsdrntg, nltfldns hn jrê kn vjgmn‘, ns=

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Tj lf vfy gb trgcgmf y lf gpruncf Kjsdrntg, nltfldns lf hn jrê kn vjgmn. c. Tj lf vfy gb trgcgmf f lf gpruncf Kjsdrntg, nltfldns lf hn jrê kn vjgmn. d. Tj lf hn vfy kn vjgmn, nltfldns lf vfy gb trgcgmf y lf l f gpruncf Kjsdrntg. 

Bg rnspunstg dfrrndtg ns= Tj lf hn vfy kn vjgmn, nltfldns lf vfy gb trgcgmf y lf gpruncf Kjsdrntg.

Yrnoultg ;

@jlgbjzgkf

Knsdrjcg sj bg rnbgdjôl kgkg g dfltjlugdjôl ns ulg rnbgdjôl kn nqujvgbnldjg, nqujvgbnldjg, dflstruyg bg orç`jdg y bg hgtrjz kn gkygdnldjg.

Yultýg dfhf 4

Tj bf ns, gpbjqun nb gbofrjthf kn _grsegbb

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

 

,

,

.

Yrnoultg >

¶Duçb ns bg prfpjnkgk qun pfsnn bg rnbgdjôl S 8 {(7, 7), (7, 3), (7, ;), (3, 7), (3, 3), (3, ;), (4, ;)}, kn`jljkg

Jldfrrndtg

sfcrn G8{7, 3, 4, ;}6

Yultýg 9 sfcrn 7

Tnbnddjfln ulg= g. Tjhêtrjdg



c. Sn`bnxjvg d. [rglsjtjvg k. Gltjsjhêtrjdg

Bg rnspunstg dfrrndtg ns= [rglsjtjvg

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 0

Snbgdjflns dgkg nbnhnltf kn rnprnsnltgdjôl org`jdg kn ulg rnbgdjfl

Dfrrndtg Yultýg 7 sfcrn 7



 



 



 

 

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37





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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Bg rnspunstg dfrrndtg ns=

↓ Tgojtgb,

Dgrtnsjglf,, Dgrtnsjglf

↓

↓ [gcubgr,

↓ Kjgorghg kn çrcfb,

↓ Hgtrjdjgb

Yrnoultg ?

Dugb kn bfs sjoujnltns nluldjgkfs n vnrkgknrf pgrg bg hgtrjz kn gkygdnldjg kn ul kèorg`f

Dfrrndtg

Tnbnddjfln ulg= Yultýg 7 sfcrn 7

g. Nb luhnrf kn dnrfs qun gpgrndnl nl ulg `jbg ns jougb gb orgkf kn sgbjkg knb dfrrnspflkjnltn vêrtjdn. c. Bg hgtrjz kn gkygdnldjg ns sjhêtrjdg d. Nb luhnrf kn dnrfs qun pgrndnl nl ulg kntnrhjlgkg dfbuhlg ns jougb gb orgkf kn nltrgkg knb dfrrnspflkjnltn vêrtjdn. k. Nb luhnrf kn ulfs qun gpgrndnl nl ulg `jbg ns jougb gb orgkf kn sgbjkg knb dfrrnspflkjnltn vêrtjdn.



Bg rnspunstg dfrrndtg ns= Nb luhnrf kn ulfs qun gpgrndnl nl ulg `jbg ns jougb gb orgkf kn sgbjkg knb dfrrnspflkjnltn vêrtjdn.

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 5

Dfrrndtg

^lg rnbgdjôl S sfcrn ul dflmultf G rndjcn nb lfhcrn kn VVVVVVVVVVVVV sj pgrg tfkf (x , y ) Ћ g S dfl x ≩ y sn tjnln qun ( y , x ) lf Ћ g S

Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Gltjsjhêtrjdg



c. [rglsjtjvg d. Sn`bnxjvg k. Tjhêtrjdg

Bg rnspunstg dfrrndtg ns= Gltjsjhêtrjdg

Yrnoultg :

Dfrrndtg

^lg VVVVVVVVVVVVVV S kn ul dflmultf U g ul dflmultf Z ns ul sucdflmultf knb prfkudtf dgrtnsjglf U x Z. Tj (x, y) Ћ S sn nsdrjcn x S y y sn kjdn qun x nstg rnbgdjflgkf dfl y.

Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Snbgdjôl rn`bnxjvg c. Snbgdjôl kn nqujvgbnldjg d. Snbgdjôl cjlgrjg  k. Snbgdjôl kn frknl pgrdjgb

Bg rnspunstg dfrrndtg ns= Snbgdjôl cjlgrjg

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

>/79

 

5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 79

Tnbnddjflns nb org`f dfrrnspflkjnltn g bg hgtrjz kn gkygdnldjg sjoujnltn=

Dfrrndtg Yultýg 7 sfcrn 7

9379 3937 9397 7779  

Tnbnddjfln ulg=

g.



c.

d.

k.

Bg rnspunstg dfrrndtg ns=

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 77

Nb djrdujtf bôojdf duyg sgbjkg ns ulf sôbf duglkf tfkgs sus nltrgkgs sfl ulfs, sn bbghg=

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Dfhpunrtg FS c. Dfhpunrtg LFS d. Jlvnrsfr. k. Dfhpunrtg GLK. 

Bg rnspunstg dfrrndtg ns= Dfhpunrtg GLK.

Yrnoultg 73

Bg lnogdjôl kn bg nxprnsjfl= ‒Nstfy dursglkf Kjsdrntg y lf nstukjf nl bg uljvnrsjkgk‘, ns=

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Lf nstfy dursglkf Kjsdrntg f nstukjf nl bg uljvnrsjkgk.  c. Nstfy dursglkf Kjsdrntg f lf nstukjf nl bg uljvnrsjkgk. d. Lf nstfy dursglkf Kjsdrntg y nstukjf nl bg uljvnrsjkgk.

Bg rnspunstg dfrrndtg ns= Lf nstfy dursglkf Kjsdrntg f nstukjf nl bg uljvnrsjkgk.

Yrnoultg 74

Bg dfrrndtg kn`jljdjôl kn orgkf kn ul org`f ns=

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Luhnrf kn grjstgs qun sgbnl kn ul lfkf c. Luhnrf kn grjstgs qun nltrgl g ul lfkf d. Dgltjkgk kn lfkfs vndjlfs k. Luhnrf kn grjstgs qun nltrg f sgbnl kn ul lfkf 

Bg rnspunstg dfrrndtg ns= Luhnrf kn grjstgs qun nltrg f sgbnl kn ul lfkf

Yrnoultg 7;

Bg rndjprfdg kn bg prfpfsjdjfl= Tj tnlof tjnhpf y lf nstfy knhgsjgkf dglsgkf, nltfldns jrê g bg tjnlkg.

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Tj lf tnlof tjnhpf y nstfy knhgsjgkf dglsgkf, nltfldns lf jrê g bg tjnlkg. c. Tj lf nstfy knhgsjgkf dglsgkf y tnlof tjnhpf, nltfldns jrê g bg tjnlkg. d. Tj vfy g bg tjnlkg , nltfldns tnlof tjnhpf y lf nstfy knhgsjgkf dglsgkf.  k. Tj tnlof tjnhpf, nltfldns jrê g bg tjnlkg y lf nstfy knhgsjgkf dglsgkf.

Bg rnspunstg dfrrndtg ns= Tj vfy g bg tjnlkg , nltfldns tnlof tjnhpf y lf nstfy knhgsjgkf dglsgkf.

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 7>

Dfrrndtg Yultýg 7 sfcrn 7

Jlkjdgr duçb ns bg rnobg kn jl`nrnldjg qun sn utjbjzô nl nb pgsf Lf. ;, knb sjoujnltn Grouhnltf. Grouhnltf. Knhfstrgr= r (7) p ↓ q

Y

(3) ~q

Y

(4) ~p ↓ ~ (~r)

Y

(;) ~p

(

(>) ~ (~ r)

(Y,Y) (4,;)

(0) r

) (7,3)

(K,L) (>)

Tnbnddjfln ulg= g. YY c. TE d. [[ 

Bg rnspunstg dfrrndtg ns= [[

Yrnoultg 70

Dfrrndtg Yultýg 7 sfcrn 7

Ns ulg rnprnsnltgdjôl hgtrjdjgb kn ulg rnbgdjôl. Nl nstg, bfs nbnhnltfs knb prjhnr dflmultf dfrrnspflknl g bgs `jbgs f bfs rnlobflns kn bg hgtrjz, hjnltrgs qun bgs dfbuhlgs pnrtnlndnl g bfs nbnhnltfs knb snoulkf dflmultf. Tj kfs nbnhnltfs nstçl rnbgdjflgkfs sfl rnprnsnltgkfs dfl ul 7 (nl bg jltnrsnddjôl `jbg-dfbuhlg dfrrnspflkjnltn) y dfl ul 9 nl dgsf dfltrgrjf.

Tnbnddjfln ulg= g. Hgtrjz kn jldjknldjg c. Grcfbns d. Kjorg`fs k. Hgtrjz kn rnbgdjfl 

Bg rnspunstg dfrrndtg ns= Hgtrjz kn rnbgdjfl

Yrnoultg 7?

Dfrrndtg

^lg rnbgdjôl S sfcrn ul dflmultf U rndjcn nb lfhcrn kn VVVVVVVVVVVVV sj pgrg tfkf (x , y ), (y , z) Ћ g S sn tjnln qun ( x , z ) Ћ g S.

Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Tjhêtrjdg c. [rglsjtjvg  d. Gltjsjhntrjdg k. Sn`bnxjvg

Bg rnspunstg dfrrndtg ns= [rglsjtjvg

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 75

Bg nxprnsjfl= ‒Gpbjdf Hgtnhçtjdg Kjsdrntg, sj nltjnlkf tfkf bf nstukjgkf‘, ns nqujvgbnltn g=

Dfrrndtg

 

Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Tj nltjnlkf tfkf bf nstukjgkf, nltfldns gpbjdf Hgtnhçtjdg Kjsdrntg.  c. Tj lf gpbjdf tfkf bf nstukjgkf, nltfldns gprnlkf Kjsdrntg. d. Tj gpbjdf Hgtnhçtjdg Kjsdrntg, nltfldns nltjnlkf tfkf bf nstukjgkf. k. Tj lf gpbjdf Hgtnhçtjdg Kjsdrntg, nltfldns lf nltjnlkf tfkf bf nstukjgkf.

Bg rnspunstg dfrrndtg ns= Tj nltjnlkf tfkf bf nstukjgkf, nltfldns gpbjdf Hgtnhçtjdg Kjsdrntg.

Yrnoultg 7:

Snbgdjflns dgkg nbnhnltf kn bg dfbuhlg dfl nb vgbfr nqujvgbnltn kn bg knrndeg

Dfrrndtg Yultýg 3 sfcrn

GD.5C.C7.7?

 

7?3.0>.5:.34

 

79.9.39.7

 

3

Bg rnspunstg dfrrndtg ns= GD.5C.C7.7? ↓ 7?3.74:.7??.34, 7?3.0>.5:.34 ↓ GD.;7.>:.7?, 79.9.39.7 ↓ 9G.99.7;.97

Yrnoultg 39

Jlkjdgr duçbns sfl bgs rnobgs kn jl`nrnldjgs qun sn utjbjzgrfl nl bfs pgsfs= ;, >, 0 y ?, rnspndtjvghnltn knb

Dfrrndtg

sjoujnltn Grouhnltf.

Yultýg 7 sfcrn 7

Knhfstrgr= ~ Y (7) (Y v W) ↓ (S v T)

Y

 

(3) (S v T) ↓ ~ [

Y

 

(4) [

Y

(;) ~(S v T)

( ) 3, 4

 

(>) ~ (Y v W)

( ) 7, ;

 

(0) (~ Y \ ~W)

( )>

 

(?) ~ Y

( )0

Tnbnddjfln ulg= g. TE, K'HFSOGL, [[, T c. [[, TE, K'HFSOGL, T d. [[, [[, K'HFSOGL, T  k. TE, [[, K'HFSOGL, T

Bg rnspunstg dfrrndtg ns= [[, [[, K'HFSOGL, T

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

:/79

 

5/73/3939

NUGHNL @JLGB 3939-4= Snvjsjôl knb jltnltf

Yrnoultg 37

Sndfrrjkf knb çrcfb nl pfstfrknl pgrg bg `jourg `jourg sjoujnltn=

Jldfrrndtg Yultýg 9 sfcrn 7

Tnbnddjfln ulg= g. c,g,n,d,o,`,k c. g,c,d,n,`,o,k d. g,c,d,k,n,`,o



k. c,n,o,`,d,k,g

Bg rnspunstg dfrrndtg ns= c,n,o,`,d,k,g

Yrnoultg 33

Bg sgbjkg kn ulg dfhpunrtg FS ns 9 duglkf....

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. Ghcgs nltrgkgs nstçl nl 9.  c. Ghcgs nltrgkgs nstçl nl 7. d. Dugbqujnrg f ghcgs nltrgkgs nstçl nl 9. k. Dugbqujnrg f ghcgs nltrgkgs nstçl nl 7.

Bg rnspunstg dfrrndtg ns= Ghcgs nltrgkgs nstçl nl 9.

Yrnoultg 34

Ns gqunbbg trgyndtfrjg nl bg qun sn rndfrrnl tfkgs bgs grjstgs kn bg orç`jdg.

Dfrrndtg Yultýg 7 sfcrn 7

Tnbnddjfln ulg= g. [rgyndtfrjg kn Eghjbtfl c. Gbofrjthf kn @bnury d. [rgyndtfrjg nubnrjglg  k. Djrdujtf nubnrjglf

Bg rnspunstg dfrrndtg ns= [rgyndtfrjg nubnrjglg

ettps=//nvg.ulgpnd.nku.kf/hffkbn/hfk/qujz/rnvjnw.pep6gttnhpt8>;5059&dhjk8?9:93;#qunstjfl-0735:>-37

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