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…”