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Question
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Solution
~[(~p ∧ q) ∧ (~q ∨ ~r)]
≡ ~(~p ∧ q) ∨ ~(~q ∨ ~r) ...[Negation of conjunction]
≡ [~(~p) ∨ ~q] ∨ [~(~q) ∧ ~(~r)] ...[Negation of conjunction and disjunction]
≡ (p ∨ ~q) ∨ (q ∧ r) ...[Negation on negation]
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