1.

p ∧ (p → q) is logically equivalent to (A) p ∨ q (B) ~p ∨ q (C) p ∧ q (D) p ∨ ~q

Answer»

Correct option: (C) p ∧ q 

p ∧ (p → q)

≡ p ∧ (~p ∨ q) ….[Conditional law]

≡ (p ∧ ~p) ∨ (p ∧ q) ….[Distributive law]

≡ F ∨ (p ∧ q) ….[Complement law]

 p ∧ q ….[Identity law]



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