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Question
Using the rules in logic, write the negation of the following:
(p ∨ q) ∧ (q ∨ ∼r)
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Solution
The negation of (p ∨ q) ∧ (q ∨ ∼r) is
∼ [(p ∨ q) ∧ (q ∨ ∼r)]
≡ ∼(p ∨ q) ∨ ∼(q ∨ ∼r) .....(Negation of conjunction)
≡ (∼p ∧ ∼q) ∨ [∼q ∧ ∼(∼r)] ...............(Negation of disjunction
≡ (∼p ∧ ∼q) ∨ (∼q ∧ r) ...........(Negation of negation)
≡ (∼q ∧ ∼p) ∨ (∼q ∧ r) ..........(Commutative law)
≡ (∼q) ∧ (∼p ∨ r) ..........(Distributive Law)
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