Question

Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers.

(a) x = -1, y = 17

(b) x = -2  y = 8

(c) Both x = -1, y = 17 and x = -2  y = 8

(d) Does not have any counter example

The question was posed to me in an online quiz.

I need to ask this question from Logics topic in division The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

Correct choice is (c) Both x = -1, y = 17 and x = -2  y = 8

For explanation: Putting x=-1, y=17; -17>17 which is wrong. Putting x=-2, y=8; -16>8 which is wrong.