I just need my solution checked since I'm not sure if it's valid, especially the final statement
Show $p \Rightarrow (\neg(q \land \neg p))$ is a tautology by assuming:
$u \Rightarrow v$ is logically equivalent to $\neg u \lor v$
$\neg(q \land \neg p))$ is logically equivalent to $\neg q \lor p$ (by De Morgan's law),
so $\neg q \lor p$ is logically equivalent to $q \Rightarrow p$ (given by the question) hence $p \Rightarrow (q \Rightarrow p)$ and therefore $p$ is a tautology?