Answer to Question #314212 in Discrete Mathematics for narcky

Question #314212

show that ~p --> (q --> r ) and q --> (p v r) are logically equivalent



1
Expert's answer
2022-03-19T04:09:23-0400

¬p(qr)=p(qr)=p(¬qr)=p¬qrq(pr)=¬q(pr)=p¬qr\lnot p\rightarrow \left( q\rightarrow r \right) =p\lor \left( q\rightarrow r \right) =p\lor \left( \lnot q\lor r \right) =p\lor \lnot q\lor r\\q\rightarrow \left( p\lor r \right) =\lnot q\lor \left( p\lor r \right) =p\lor \lnot q\lor r

We obtain the same expressions, thus the formulae are logically equivalent.


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