Question

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

Answer 1

$\lnot p\rightarrow \left( q\rightarrow r \right) =p\lor \left( q\rightarrow r \right) =p\lor \left( \lnot q\lor r \right) =p\lor \lnot q\lor r\\q\rightarrow \left( p\lor r \right) =\lnot q\lor \left( p\lor r \right) =p\lor \lnot q\lor r$

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