# Absorption Laws (Logic)

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

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