Solution:Let's evaluate each of the options-
(A)- P(0)- Substituting 0 for x, we get 0 = 0² , which is true. So, P(0) is true.
(B) P(1)- Substituting 1 for x, we get 1 = 1² , which is true. So, P(2) is true.
(C) P(2)- Substituting 2 for x we get 2 = 2² .Which is false. So, P(2) is false.
(D) ∃x P(x)- This statement means ''There exits an integer x such that x = x² . ''Since this is not true for any integer except 0 and 1, This statements is false.
(E) ∀x P(x)- This statement ''for all integer x, x = x² . ''Since this is only true for x = 0 and 1, and false for all other integer, this statement is false.
So, the correct option is (c).