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Lecture

inclass3_solns.pdf


Department
Math & Comp Sci
Course Code
MACM 101
Professor
Bobby Chan

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Name: StudentID:
1. Establishthevalidity(orinvalidity)ofthefollowingstatements.Ifvalid,showusingthelaws
oflogic.Otherwisegiveacounterexample:
a. p(p→q)
¬qr.
r
b. p→(q→r)
p¬s
t→q
s.
¬r→¬t
c. p¬q
¬q
p→(q→r)
¬r
2. Lettheuniversebemadeupofallshapes
r(x)=xisarectangle
s(x)=xisasquare
t(x)=xisatriangle
h(x)=allsidesofxareequal
Whatisthetruthvalueof:
a. x(¬r(x)s(x))
b. x(h(x)→s(x))
3. LetP(x,y)=“xhasbeeninclassroomy”.Write“Thereisastudentwhohasbeeninevery
classroomatFIC”asaquantifiedstatement.Remembertogivetheuniverseofeach
variable.
4. Determinethetruthvalueof:(intheuniverseofallintegers)
a. nmp(p=(m+n)/2)
b. nm(n+m=4nm=4)
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