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