Predicate Logic and universal and existential quantifiers

Question

Let P(x): x2/2=x

 

    Find the following then identify their truth values with solution.

    1. P (1)

    2. P (2)

    3. ∀n,P(n)

    4. ∃n,P(n)

Answer 1

1) False: x²/2=½, so since ½≠1 and x=1, x²/2≠x

2) True: x²/2=4/2=2=x, so x²/2=x

3) False because (1) is false, so P cannot be true ∀n

4) True because (2) is true and ∃n, since n=x=2 is an example (another example would be n=0)