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Question
Using the rule of negation write the negation of the following with justification.
(p ∨ ∼ q) ∧ r
Solution
The negation of (p ∨ ∼ q) ∧ r is
∼ [(p ∨ ∼ q) ∧ r] ≡ (p ∨ ∼ q) ∨ ∼ r .........(Negation of conjunction)
≡ [∼ p ∧ ∼ (∼ q)] ∨ ∼ r ......(Negation of disjunction) ≡ (∼ p ∧ q) ∨ ∼ r ...........(Negation of negation)
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