show that ~p --> (q --> r ) and q --> (p v r) are logically equivalent
¬p→(q→r)=p∨(q→r)=p∨(¬q∨r)=p∨¬q∨rq→(p∨r)=¬q∨(p∨r)=p∨¬q∨r\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¬p→(q→r)=p∨(q→r)=p∨(¬q∨r)=p∨¬q∨rq→(p∨r)=¬q∨(p∨r)=p∨¬q∨r
We obtain the same expressions, thus the formulae are logically equivalent.
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