Which of the following statement are truth statements if universe of disclosure is set of integers :…
(A) is true because the square of any integer is non-negative. (C) is true because \(n^2 - n = n(n-1)\) is a product of two consecutive integers, which is never negative (it…
Choose your answer
Which of the following statement are truth statements if universe of disclosure is set of integers :
(A) ∀n (n² ≥ 0)
(B) ∃n (n² = 2)
(C) ∀n (n² ≥ n)
(D) ∃n (n² < 0)
Answer and explanation
Correct answer D
(A) is true because the square of any integer is non-negative. (C) is true because is a product of two consecutive integers, which is never negative (it is zero for n = 0 and n = 1 and positive otherwise). (B) is false because 2 is not a perfect square, and (D) is false because no integer has a negative square, so only (A) and (C) are true.
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UGC NET Computer Science and Applications