Absorption Laws (Logic)/Conjunction Absorbs Disjunction/Proof by Truth Table
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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.
$\begin{array}{|ccccc||c|} \hline p & \land & (p & \lor & q) & p \\ \hline \F & \F & \F & \F & \F & \F \\ \F & \F & \F & \T & \T & \F \\ \T & \T & \T & \T & \F & \T \\ \T & \T & \T & \T & \T & \T \\ \hline \end{array}$
$\blacksquare$