Absorption Laws (Logic)

This proof is about Absorption Laws in the context of 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

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

Also see

• Absorption Laws (Set Theory)
• Absorption Laws (Lattice Theory)