Show $p \lor (p \land q ) \equiv p $ using equivalences

Question

I am trying to show $p \lor (p \land q ) \equiv p $ using equivalences.

I have tried many replacements (e.g. distributivity and de Morgans) but cannot see a way to simplify the left hand side that reduces to $p$.

Here are is a list of logical equivalences from wikipedia.

I know that this statement is true (via truth tables), but I cannot derive this using equivalences. Ideas appreciated.

Answer 1

It's in the list ... but some texts like to derive it as follows:

$$p \lor (p \land q) \equiv (p \land \top) \lor (p \land q) \equiv p \land (\top \lor q) \equiv p \land \top \equiv p$$

Answer 2

This is listed, verbatim, as one of the absorbtion laws in the wikipedia page you linked.