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The statement among the following that is a tautology is : (1) A ∨ (A ∧ B) (2) A ∧ (A ∨ B) (3) B → [A ∧ (A → B)] (4) [A ∧ (A → B)] → B

1. A ∨ (A ∧ B)
2. A ∧ (A ∨ B)
3. B → [A ∧ (A → B)]
4. [A ∧ (A → B)] → B

Correct answer: [A ∧ (A → B)] → B

Solution

The statement [A ∧ (A → B)] → B is a tautology because it asserts that if A is true and A implies B, then B must also be true, which holds in all possible truth scenarios.

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