Are these logically equivalent p q q p True False Select The

Are these logically equivalent? p q (q p) True False Select The best translation: \"Neither Abby nor Johnny are going to The party, but Nancy and Pam are\" (~A ~J) (N P) (A J) N P ~(A J) (N P) (A J) (N P) Is this argument valid? True for Valid, False for Invalid: p q q r r True False

Solution

1) p and ~q

~ (q or ~p) = ~(~p) and ~(q) by Demorgan\'s law

= p and ~q

Hence, they are equivalent

2) ~(A v J) and (N and P). The 4th option is correct

3) p-> q, ~q and r, therefore r

This argument is True. ~q and r implies r is true. Therefore the conclusion follows from the premises.