Question

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

∃ x ∈ A such that x – 8 = 1

Answer 1

This means there exists an element x in A such that x − 8 = 1. Solving for x:

∴ x − 8 = 1

∴ x = 1 + 8

∴ x = 9

Check if x = 9 belongs to A:

The set A = {3, 5, 7, 9, 11, 12} contains 9.

There exists an x ∈ A such that x − 8 = 1

Clearly x = 9 ∈ A satisfies x − 8 = 1. So the given statement is true, hence its truth value is T.