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*…”