Absorption (Propositional Logic)

Definition

Absorption (Propositional Logic)

Absorption is the pair of equivalences in which a formula absorbs a compound of itself and another formula:

$$P\vee (P\wedge Q)\equiv P,P\wedge (P\vee Q)\equiv P.$$

In $P\vee (P\wedge Q)$ the conjunct $P\wedge Q$ can never make the disjunction true when $P$ is false, and adds nothing when $P$ is true; the whole expression always equals $P$. The second law is its dual, obtained by swapping $\vee$ and $\wedge$.