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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.Note: symmetry is not the exact opposite of antisymmetry (aRb and bRa implies b = a). There are relations which are both symmetric and antisymmetric (equality and its subrelations, including, vacuously, the empty relation), there are relations which are neither symmetric nor antisymmetric (''preys on'' in biological sciences), there are relations which are symmetric and not antisymmetric (congruence modulo n), and there are relations which are not symmetric but are antisymmetric ("is less than or equal to").equivalence relation - A symmetric relation that is also transitive and reflexive.