NTA UGC NET Dec 2023 Paper-2
May 23, 2024NTA UGC NET Dec 2023 Paper-2
May 23, 2024NTA UGC NET Dec 2023 Paper-2
| Question 24 |
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
(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
| (A), (B) and (E) Only | |
| (A), (B) and (C) Only | |
| (A), (B) and (D) Only | |
| (B), (C) and (D) Only |
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
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
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