Absorption Laws (Logic)

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This proof is about the absorption laws in propositional logic. For other uses, see Absorption Laws.

Theorem

For any two propositions $p$ and $q$, we have:


Conjunction Absorbs Disjunction

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


Disjunction Absorbs Conjunction

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


Also see