What I've been told is that an inconsistent set of propositions is irrelevant in propositional logic because if it derives a contradiction, then you can't derive anything else from it, but here's my doubt:
Take $\Gamma = \{p \land q, \neg(p \land q)\}.$ This clearly derives a contradiction. But by $(\land E)$, can't I derive both p and q from $p \land q$, such that I can say that $\Gamma \vdash p$ and $\Gamma \vdash q$?