Reciprocal Relationship

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

Notation

The reciprocal relationship of a relationship [latex]\mathcal{R}[/latex] is denoted by [latex]\mathcal{R}^{-1}[/latex].

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…"

Reciprocal Relationship

Notation

Example

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