Given an example of a conjunction

| August 30, 2017

(1)Prove, using propositional calculus, that

~((PvQ)>R) (P^~R)v(Q^~R)

(2) Given an example of a conjunction that is a tautology and a disjunction that is a contradiction

(3) Negate and put into positive form

a: (Ǝx)[Q(x)>P(x)]

b: (∀x)(Ǝy)(P(x)^Q(x))

c: (Ǝx)(Ǝy)(P(x)vQ(x,y))

d: [(Ǝx)(~R(x))]v[(∀x)(Q(x)~P(x))]

(4) Let x and y be two integers. Prove that x^2+xy+y^2 is divisible by 9 if and only if x and y are divisible by 3. (Please provide the (=>) proof only, proof by contradiction)

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