# Reciprocal Relationship

## Reciprocal Relationship

The reciprocal relationship of a relationship $$\mathcal{R}$$ of X in Y is the relationship of Y in X, such that, for all the elements of the domain of $$\mathcal{R}$$, if y = $$\mathcal{R}$$(x), then x = $$\mathcal{R}^{-1}$$(y).

### Notation

The reciprocal relationship of a relationship $$\mathcal{R}$$ is denoted by $$\mathcal{R}^{-1}$$.

### Example

The reciprocal relationship of a relationship “…divides without remainder…” on the set of whole numbers is the relationship “… is a non-zero multiple of…”