Commutativity (Propositional Logic)

Definition

Commutativity (Propositional Logic)

Commutativity is the property of the connectives $\vee$ and $\wedge$ that the order of two formulas is irrelevant:

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

For every interpretation $v$,

$$v(P\vee Q)=v(Q\vee P),v(P\wedge Q)=v(Q\wedge P).$$

Both connectives depend only on the multiset of operand truth values, not on their order.