Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Proof by Truth Table

Theorem

$p \land \paren {p \lor q} \dashv \vdash p$

Proof

We apply the Method of Truth Tables.

As can be seen by inspection, the appropriate truth values match for all boolean interpretations.

$\begin{array}{|ccccc||c|} \hline p & \land & (p & \lor & q) & p \\ \hline \F & \F & \F & \F & \F & \F \\ \F & \F & \F & \T & \T & \F \\ \T & \T & \T & \T & \F & \T \\ \T & \T & \T & \T & \T & \T \\ \hline \end{array}$

$\blacksquare$