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The negation of (p ∨ ~q) ∧ q is (A) (~p ∨ q) ∧ ~q  (B) (p ∧ ~q) ∨ q 

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The negation of (p ∨ ~q) ∧ q is

(A) (~p ∨ q) ∧ ~q 

(B) (p ∧ ~q) ∨ q 

(C) (~p ∧ q) ∨ ~q 

(D) (p ∧ ~q) ∨ ~q

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1 Answer

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Correct option: (C) (~p ∧ q) ∨ ~q 

~[(p ∨ ~q) ∧ q] ≡ ~(p ∨ ~q) ∨ ~q ….[De Morgan’s Law]

≡ (~p) ∧ [~(~q)] ∨ ~q

≡ (~p ∧ q) ∨ ~q

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