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Which of the following statements is always true for every truth assignment?

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

[A and (A->B)] -> B is the modus-ponens schema and is true under every assignment. A or (A and B) reduces to A and A and (A or B) reduces to A, neither a tautology; B -> [A and (A->B)] fails when B is true and A is false.

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