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Use the laws of logic to show that [(p→q)Ʌ~q]→~q is a tautology. |
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Answer» (p→q) ∧ ~ q → ~ q ≡ ~((p→q)∧ ~q) v ~q ( ∵ p → q ≡ ~p v q) ≡ ~ ((~p v q) ∧~q ) ≡ ~((~p∧~q) v (q ∧ ~q)) v ~q ≡ ~ ((~p ∧ ~p ) v F) v ~q ≡ ~ (~p∧~p) v ~q ≡ (~(~p) v ~(~q)) v ~q ≡ (p v q) v ~q ≡ p v (q v ~q) ≡ p v T ≡ T Hence proved |
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