Question

“The product of two negative real numbers is not negative.” Is given by?

(a) ∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

(b) ∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

(c) ∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

(d) ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

This question was posed to me in an online quiz.

Question is taken from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

Right choice is (d) ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

Explanation: For every negative real number x and y, the product of these integer is positive.