Which of the following statement are truth statements if universe of disclosure is set of integers :

(A) ∀n(n2 ≥ 0)

(B) ∃n(n= 2)

(C) ∀n(n2 ≥ n)

(D) ∃n(n2 < 0)

Choose the correct answer from the options given below:

This question was previously asked in
UGC NET Computer Science (Paper 2) 07 Dec 2023 Official Paper
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  1. (A) and (B) Only
  2. (B) and (C) Only
  3. (C) and (D) Only
  4. (A) and (C) Only

Answer (Detailed Solution Below)

Option 4 : (A) and (C) Only
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Detailed Solution

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The correct answer is (A) and (C) Only

EXPLANATION:

  • (A) ∀n(n2 ≥ 0):
    • This statement is true because the square of any integer is always greater than or equal to zero.
  • (B) ∃n(n2 = 2):
    • This statement is false. No integer squared equals 2.
  • (C) ∀n(n2 ≥ n):
    • This statement is true for all integers because the square of any integer is greater than or equal to the integer itself.
  • (D) ∃n(n2 < 0):
  • This statement is false because the square of any integer cannot be less than zero.

So, the correct option is: (A) and (C) Only.

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