###### NTA UGC NET Dec 2023 Paper-2

May 23, 2024###### Question 17366 – NTA UGC NET Dec 2023 Paper-2

May 23, 2024# Question 17364 – NTA UGC NET Dec 2023 Paper-2

The statement P(x): “x=x^2” .If the universe of disclosure consists of integers, which of the following have truth values

(A) P(0)

(B) P(1)

(C) P(2)

(D) ∃x P(x)

(E) ∀x P(X)

Choose the correct answer from the options given below

Correct Answer: C

Question 24 Explanation:

(A) P(0): True, because 0 = 0^2.

(B) P(1): True, because 1 = 1^2.

(C) P(2): False, because 2 ≠ 2^2.

(D) ∃x P(x): True, because there exists at least one integer x (namely, 0 and 1) for which P(x) is true.

(E) ∀x P(x): False, because not all integers satisfy the condition x = x^2.

Therefore, only statements (A), (B), and (D) have truth values in the given universe of discourse, making the answer

(B) P(1): True, because 1 = 1^2.

(C) P(2): False, because 2 ≠ 2^2.

(D) ∃x P(x): True, because there exists at least one integer x (namely, 0 and 1) for which P(x) is true.

(E) ∀x P(x): False, because not all integers satisfy the condition x = x^2.

Therefore, only statements (A), (B), and (D) have truth values in the given universe of discourse, making the answer

(A), (B) and (E) Only

(A), (B) and (C) Only

(A), (B) and (D) Only

(B), (C) and (D) Only

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