Show that the following logical implication is True?

Question

It is True, I did the truth tables... but it's just hard to prove it. I tried simplifying both sides but still it wasn't a match?

Answer 1

$$\begin{align} ((x\to y)\lor\lnot z)\to(x\land \lnot(y \to z)) &\equiv \lnot((x\to y)\lor\lnot z)\lor (x\land \lnot(y \to z)) \\ &\equiv \lnot( \lnot x\lor y \lor\lnot z)\lor (x\land \lnot(\lnot y \lor z))\\ &\equiv (x\land \lnot y\land z)\lor (x\land ( y \land \lnot z))\\ &\equiv (x\land \lnot y \land z) \lor (x\land y \land \lnot z)\\ &\equiv x\land ((\lnot y \land z) \lor (y \land \lnot z))\\ &\equiv x\land ((\lnot y \leftrightarrow z)\\ \end{align}$$