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Question
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x – 8 = 1
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Solution
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.
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