Can this binary-expression be simplified?

Question

Let $p = (a \land b) \lor (c \land d)$ where $\land$ and $\lor$ are bitwise AND and OR operators respectively. Can $p$ be simplified?

Answer 1

Since the expression is sensible on every value (for example, if $b$ is true and $c \land d$ is false, then we need $a$ to know if the full expression is true or false) and it already uses each value only one time, we can't simplify it.