# Rule of Association

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## Theorem

## 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

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

### 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:

so it is wise to be aware of the context.

## Also see

## Sources

- 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (previous) ... (next): $3.2$: The Rule of Replacement