Associativity (Propositional Logic)

Definition

Associativity (Propositional Logic)

Associativity is the property of the connectives $\vee$ and $\wedge$ that the grouping of operands is irrelevant:

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

Brackets may therefore be omitted in longer chains: $P\vee Q\vee R$ and $P\wedge Q\wedge R$ are unambiguous. Together with commutativity, this makes $\vee$ and $\wedge$ behave like multi-way connectives.