Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Proof 1

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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.

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

$\blacksquare$