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

Theorem

 * $p \land \left({p \lor q}\right) \dashv \vdash p$

Proof
We apply the Method of Truth Tables.

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

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