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Which one of the following statements is not a tautology ?

1. (p → (p ∨ q))
2. ((p ∧ q) → (¬p) ∨ q)
3. ((p ∧ q) → p)
4. ((p ∨ q) → (p ∨ (¬q)))

Correct answer: ((p ∨ q) → (p ∨ (¬q)))

Solution

The statement ((p ∨ q) → (p ∨ (¬q))) is not a tautology because there are truth assignments for p and q where the implication does not hold true, specifically when p is false and q is true.

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