Prove that $$[\neg p \land (p \lor q)] \to q$$ is TRUE using logic laws.
Here is how I solved it:
$[\neg p \land (p \lor q)] \to q$
An understood logical equivalence
$[\neg \neg p \land \neg(p \lor q)] \lor q$
$[p \land \neg(p \lor q)] \lor q)$
De Morgan's law
$[ p \land (\neg p \land \neg q)] \lor q$
$[(p \land \neg p) \land \neg q] \lor q$
$(F \land \neg q) \lor q$
$F \lor q$
$ q $
The problem is that to my understanding, this doesn't necessarily prove the statement to be true, and I am not sure where I have gone wrong.