Is $(\neg p \lor (p \rightarrow q)) \rightarrow\neg p$ a Tautology? According to the truth table, following is is a Tautology or not?
$(\neg p \lor (p \rightarrow q)) \rightarrow \neg p$
Hint: See $p = F $ and $q = T $.
The whole implication is false when $(p \vee (p \rightarrow q))$ is true and $p$ is false. In this case, $p \rightarrow q$ must be true. This happens if $q$ is true or false. So that is not a tautology.