# Rule of Commutation

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## Contents

## Theorem

## Conjunction

### Formulation 1

- $p \land q \dashv \vdash q \land p$

### Formulation 2

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

## Disjunction

### Formulation 1

- $p \lor q \dashv \vdash q \lor p$

### Formulation 2

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

Its abbreviation in a tableau proof is $\text{Comm}$.

## Also known as

The **rule of commutation** is also known as the **commutative 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

## Technical Note

When invoking the **Rule of Commutation** in a tableau proof, use the `{{Commutation}}`

template:

`{{Commutation|line|pool|statement|depends|type}}`

where:

`line`

is the number of the line on the tableau proof where Rule of Commutation is to be invoked`pool`

is the pool of assumptions (comma-separated list)`statement`

is the statement of logic that is to be displayed in the**Formula**column,**without**the`$ ... $`

delimiters`depends`

is the line (or lines) of the tableau proof upon which this line directly depends`type`

is the type of Rule of Commutation: specifically`Disjunction`

or`Conjunction`

, whose link will be displayed in the**Notes**column.

## Sources

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