Which of the following statements are true if the universe of discourse is the set of integers? (A) ∀n (n² ≥ 0) (B) ∃n (n² = 2) (C) ∀n (n² ≥ n) (D) ∃n (n² < 0)

1. A(A) and (B) Only
2. B(B) and (C) Only
3. C(C) and (D) Only
4. D(A) and (C) Only

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Show answer & explanation

Correct answer: D. (A) and (C) Only

Explanation

Every square is non-negative (A true), so D is false. No integer squares to 2 (B false). For integers, n² ≥ n always holds (for n ≤ 0 trivially, for n ≥ 1 since n ≥ 1). So A and C.