If the universe of discourse is the set of integers, which of the following are TRUE?
(A) ∀n ∃m (n² < m)
(B) ∃n ∀m (n < m²)
(C) ∃n ∀m (nm = m)
(D) ∃n ∃m (n² + m² = 6)
(E) ∃n ∃m (n + m = 4 ∧ n − m = 1)
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Correct answer: A. (A), (B) and (C) Only
Explanation
A: take m = n² + 1, so it is true. B: n = −1 < m² for every m, true. C: n = 1, true. D: no two integer squares add to 6, false. E: forces n = 2.5, false. So A, B and C. (Some published keys print option B, but statement A is clearly true.)More Discrete Structures and Optimisation questions
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