Which of the following are tautology? → → → →
(A) (P (P Q)) (P Q) → → → ∨
(B) ((P Q) Q) (P Q) ∨¬ → → ∨¬ →
(C) ((P P) Q) ((P P) R) → ∧¬ → → ∧¬
(D) (Q (P P)) (R (P P))
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: C. (A) and(B) Only
Explanation
(A) P → (P → Q) ≡ P → Q, so A is X → X. (B) (P → Q) → Q ≡ P ∨ Q, so B is X → X. (C) reduces to Q → R and (D) to ¬Q → ¬R, neither a tautology.
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