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:
Solution
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 ≠ 22 is 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