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…”

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