Simplify $(p\land q)\lor(p\land \neg q)$

Question

So I was asked to simplify this statement $S$:

$$(p \land q) \lor (p \land \neg q)$$

My understanding is that it needs to have a similar truth table, though I'm not sure if that's exactly right. I tried simplifying it, but I can't think of any way to make it simpler and logically equivalent.

Any help is appreciated.

Answer 1

Using the distributive rule on the first line, $$\begin{align} (p\land q) \lor (p \land \lnot q) &\equiv p \land\underbrace{(q \lor \lnot q)}_{\large\text{true}}\\ & \equiv p\end{align}$$