The statement P(x): "x=x²". If the universe of disclosure consists of integers, what are 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:

Question

Question

This question was previously asked in

UGC NET Computer Science (Paper 2) 07 Dec 2023 Official Paper

Answer 1

The correct answer is (A), (B) and (D) Only

EXPLANATION:

(A) P(0):
- 0 = 0² is true, so (A) is true.
(B) P(1):
- 1 = 1² is true, so (B) is true.
(C) P(2):
- 2 ≠ 2²is false, so (C) is false.
(D) ∃x P(x):
- There exists an x such that x = x². From the previous evaluations, we can see that x = 0 and x = 1 satisfy this condition. So, (D) is true.
(E) ∀x P(x):
- For all x, x = x². This is not true for all integers, as we saw with x = 2. So, (E) is false.

Therefore, the correct answer is option:(A), (B) and (D) Only