Homework Answers
To prove:
~ p ∨ ~p ∧ q ≡ ~p∧~q
LHS:
~ p ∨ ~p ∧ q
= 1 ∧ ~p ∧ ~p ∧ q [ Identity law ]
= (~q v q) ∧ ~p ∧ ~p ∧ q [ Complement law ]
= (~p ∧ q) v (~p ∧~q) v (~p ∧~q) [ Distributive Law ]
= ~p ∧ (q ∧~q ∧~q) [ Taking ~p common ]
= ~p ∧ (1 ∧~q) [ Complement law ]
= ~p ∧~q [ Identity law ]
= RHS
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