# Rule of Association

## Conjunction

### Formulation 1

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

### Formulation 2

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

## Disjunction

### Formulation 1

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

### Formulation 2

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

## Also known as

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: