Question

Let the statement be “If n is not an odd integer then square of n is not  odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove _________

(a) ∀nP ((n) → Q(n))

(b) ∃ nP ((n) → Q(n))

(c) ∀n~(P ((n)) → Q(n))

(d) ∀nP ((n) → ~(Q(n)))

The question was posed to me in semester exam.

My enquiry is from Types of Proofs in division The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

Right answer is (a) ∀nP ((n) → Q(n))

For explanation: Definition of direct proof.