Rule of Association

Theorem

Conjunction is associative:

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

$\vdash \paren {p \land \paren {q \land r} } \iff \paren {\paren {p \land q} \land r}$

Disjunction is associative:

$p \lor \paren {q \lor r} \dashv \vdash \paren {p \lor q} \lor r$

$\vdash \paren {p \lor \paren {q \lor r} } \iff \paren {\paren {p \lor q} \lor r}$

The rule of association is also known as the associative law.

Note that this term is also used throughout mathematics in the context of addition and multiplication of numbers:

so it is wise to be aware of the context.

1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): associative law