Distributivity (Propositional Logic)

Definition

Distributivity (Propositional Logic)

Distributivity is the pair of equivalences stating that each of the connectives $\vee$ and $\wedge$ distributes over the other, for all formulas $P,Q,R$:

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

Unlike in arithmetic, where multiplication distributes over addition but not vice versa, both distributive laws hold in propositional logic.