Question

Let the statement be “If n is not an odd integer then sum of n with  some not  odd number  will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not  odd number will not be odd.” A proof by contraposition will be ________

(a) ∀nP ((n) → Q(n))

(b) ∃ nP ((n) → Q(n))

(c) ∀n~(P ((n)) → Q(n))

(d) ∀n(~Q ((n)) → ~(P(n)))

This question was addressed to me in class test.

This intriguing question comes from Types of Proofs topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

Right answer is (d) ∀n(~Q ((n)) → ~(P(n)))

Explanation: Definition of proof by contraposition.