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

Theorem

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

Proof

We apply the Method of Truth Tables.

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

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

$\blacksquare$