Question

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x is an even number.

Answer 1

The given set is A = {3, 5, 7, 9, 11, 12}

x = 3 ∈ A, x = 5 ∈ A, x = 7 ∈ A, x = 9 ∈ A, x = 11 ∈ A do not satisfy x is an even number.

It is observed that only x = 12 ∈ A satisfies the given statement ''∀ x ∈ A, x is an even number".

Hence, the given statement is not true for all the values, thus its truth value is F.