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Question
Without using truth table, show that
~ [(p ∧ q) → ~ q] ≡ p ∧ q
Solution
L.H.S.
≡ ~ [(p ∧ q) → ~ q]
≡ (p ∧ q) ∧ ~ (~ q) ....[Negation of implication]
≡ (p ∧ q) ∧ q .....[Negation of a negation]
≡ p ∧ (q ∧ q) ....[Associative law]
≡ p ∧ q .....[Idempotent law]
≡ R.H.S.
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