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Question
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
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Solution
~[(p ↔ q) v (~ q → ~ r)]
≡ ~(p ↔ q) ˄ (~ q → ~ r) ...[Negation of disjunction]
≡ [(p ˄ ~ q) v (q ∧ ~ p)] ∧ ~(~ q → ~ r) ...[Negation of double implication]
≡ [(p ˄ ~ q) v (q ˄ ~ p)] ˄ [~ q ˄ ~(~ r)] ...[Negation of implication]
≡ [(p ˄ ~ q) v (q ˄ ~ p)] ˄ (~ q ˄ r) ...[Negation of negation]
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