Question

Use the laws of logic to show that [(p→q)Ʌ~q]→~q is a tautology.

Answer 1

(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