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Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).

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Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).

(a) True

(b) False

This question was posed to me during an internship interview.

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

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The answer is False

Why? check below explanation:

There exist no integer for which x+4=x-4.

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