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Binary relation
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=== Composition === {{main|Composition of relations}} If <math>R</math> is a binary relation over sets <math>X</math> and <math>Y</math>, and <math>S</math> is a binary relation over sets <math>Y</math> and <math>Z</math> then <math>S \circ R = \{ (x, z) \mid \text{ there exists } y \in Y \text{ such that } xRy \text{ and } ySz \}</math> (also denoted by <math>R; S</math>) is the {{em|composition relation}} of <math>R</math> and <math>S</math> over <math>X</math> and <math>Z</math>. The identity element is the identity relation. The order of <math>R</math> and <math>S</math> in the notation <math>S \circ R,</math> used here agrees with the standard notational order for [[composition of functions]]. For example, the composition (is parent of)<math>\circ</math>(is mother of) yields (is maternal grandparent of), while the composition (is mother of)<math>\circ</math>(is parent of) yields (is grandmother of). For the former case, if <math>x</math> is the parent of <math>y</math> and <math>y</math> is the mother of <math>z</math>, then <math>x</math> is the maternal grandparent of <math>z</math>.
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