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A ∧ ¬(A ∨ (A ∧ T)) is always __________

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A ∧ ¬(A ∨ (A ∧ T)) is always __________

(a) True

(b) False

The question was posed to me by my college professor while I was bunking the class.

This key question is from Logics topic in chapter The Foundation: Logics and Proofs of Discrete Mathematics

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The correct answer is (b) False

Easy explanation: ≡ A ∧ ¬ (A ∨ (A ∧ T))

≡ A ∧ ¬(A ∨ A)

≡ A ∧ ¬A ≡ F.

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