COMP 232 Midterm: COMP 232 Midterm 2012 Fall

• School: Concordia University
• Department: Computer Sci.
• Course: COMP 232
• Professor: All

Document Summary

Comp232mathematicsforcomputersciencefall2012midtermexamname:totalpoints:id:/71instructions. thisisaclosedbookexam. theonlyallowedtoolisanencsapprovedcalculator. provideallanswersinthisbooklet. usepen,notpencil. donotdetachanypagesfromthisexam!(2ptsea. )10pts1. lettheuniverseofdiscoursebez+,thesetofpositiveintegers. foreachofthefollowingsentences,indicatewhetheritistrueorfalse. youget+2pointsforeachcorrectanswer,-2pointsforeachwronganswer,and0pointsfor don"tknow. however,thetotalforthisquestionwillnotbelessthat0. (a) x(cid:0)(x<0) (x 2x)(cid:1)false truedon"tknow!(b) x y(cid:0)(x+y=0) (x y=0)(cid:1)true falsedon"tknow!(c) x y(x y x+y) falsetruedon"tknow!(d) x y(cid:0)(x=3) (y=4)(cid:1) truefalsedon"tknow! (e) x y z(cid:0)(y=x+z) (z x)(cid:1)true falsedon"tknow!10ptsshared via c ourse h ero. co m. Comp232 page4of6 midtermexam(6pts)6pts6. toprovep ( q) r ( s)bycontradiction,whichofthefollowingpropositionsistheappropriateonetoprove. (cid:0)( p) q s ( r)(cid:1) false(cid:0)( p) q r ( s)(cid:1) false (cid:0)( q) p ( r) s(cid:1) false (cid:0)( q) p s ( r)(cid:1) false (cid:0)p ( q) ( r) s(cid:1) false(8pts)8pts7. |p(cid:0)(a b) (b a)(cid:1)|=|p(cid:0)(a b) (a b)(cid:1)|ifandonlyifa= orb= ora b= a=ba= orb= b= ora=b a= orb= ora=b(2ptsea. )6pts8. considerthefollowingproofthatthereisnoleast(smallest)positiverealnumber. proof:supposetothecontrarythatthereisarealnumberx,suchthatxispositiveand(a)forallpositiverealnumbersy. considerthenumberx/2. then(b)becausexispositive. hence(c),whichisacontradiction. (cid:4)in(a),(b),and(c)below, llinthecorrespondingblanksintheproof,suchthatyougetavalidproof. (a)x y(b)x/2>0(c)x x/220ptsshared via c ourse h ero. co m. Comp232 page5of6 midtermexam(2ptsea. )8pts9. thesymmetricdi erencebetweensetsaandbisde nedasa b=(a b) (b a). foreachoftheproposedidentityinvolving below,statewhethertheidentityistrueorfalse. youget+2pointsforeachcorrectanswer,-2pointsforeachwronganswer,and0pointsfor don"tknow. however,thetotalforthisquestionwillnotbelessthat0. (a)(a b) c=a (b c). false truedon"tknow!(b)(a b) (c d)=(a c) (b d). truefalsedon"tknow!(c)((a b) c) (a b c)=a b c. falsetruedon"tknow! (d)(a b) b=a b truefalsedon"tknow!. endofexam . 8ptsshared via c ourse h ero. co m.