For a relation to be reflexive: For all elements in A, they should be related to themselves. We conclude that \(S\) is irreflexive and symmetric. When is the complement of a transitive . This property tells us that any number is equal to itself. As, the relation '<' (less than) is not reflexive, it is neither an equivalence relation nor the partial order relation. We use cookies to ensure that we give you the best experience on our website. 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Using this observation, it is easy to see why \(W\) is antisymmetric. Enroll to this SuperSet course for TCS NQT and get placed:http://tiny.cc/yt_superset Sanchit Sir is taking live class daily on Unacad. This relation is called void relation or empty relation on A. Whether the empty relation is reflexive or not depends on the set on which you are defining this relation you can define the empty relation on any set X. The relation is not anti-symmetric because (1,2) and (2,1) are in R, but 12. A transitive relation is asymmetric if it is irreflexive or else it is not. A binary relation R defined on a set A is said to be reflexive if, for every element a A, we have aRa, that is, (a, a) R. In mathematics, a homogeneous binary relation R on a set X is reflexive if it relates every element of X to itself. 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