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A binary relation over a set X and a set Y is a subset of X × Y (where X × Y is the Cartesian product of X and Y). It may also be thought of as a binary function that takes as arguments an element x of X and an element y of Y and evaluates to true or false (indicating whether the ordered pair (x, y) is an element of the set which is the relation). The notations R(x,y) or xRy are used to mean "The ordered pair (x,y) is an element of binary relation R over sets X and Y". |
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A binary relation over a set X and a set Y is a subset of X × Y (where X × Y is the Cartesian product of X and Y). It may also be thought of as a binary function that takes as arguments an element x of X and an element y of Y and evaluates to true or false (indicating whether the ordered pair (x, y) is an element of the set which is the relation). The notations R(x,y) or xRy are used to mean "The ordered pair (x,y) is an element of the binary relation R". |
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* trichotomous: for all x and y in X exactly one of xRy, yRx and x = y holds |
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-- Function -- Partial order -- Equivalence relation -- |
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-- Function -- Partial order -- Total order -- Well-order -- Equivalence relation -- |
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