If the universe of disclosure is set of integers, then which of the followings are TRUE ? (A) ∀n ∃m (n²…
A is true by choosing m=n^2+1 for each integer n. B is true with n=-1, and C with n=1. D is false because integer squares cannot sum to 6. E implies n=5/2, m=3/2, which are…
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If the universe of disclosure is set of integers, then which of the followings 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)
Answer and explanation
Correct answer A
A is true by choosing m=n^2+1 for each integer n. B is true with n=-1, and C with n=1. D is false because integer squares cannot sum to 6. E implies n=5/2, m=3/2, which are not integers. Exactly A, B, C hold, selecting the correct choice; the recorded the correct choice wrongly omits the first true statement.
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UGC NET Computer Science and Applications