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Reflexive Relation|Symmetric Relation|Transitive Relation|Examples|OMR|Summary

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Explain the following (i)Reflexive Relaton (ii) symmetric Relation (ii) Anti- symmetaic relation (iv) transitive relation

Assertion and Reason type questions : Consider the following statements,p: Every reflexive relation is a symmetric relation,q: Every anti- symmetric relation is reflexive.Which of the following is/ are true?

Let M be the set of men and R is a relation is son of defined on M.Then,R is ( a) an equivalence relation (b) a symmetric relation (c) a transitive relation (d) None of these

Let S be the set of all real numbers. Then the relation R:- {(a ,b):1+a b >0} on S is: (a)an equivalence relation (b)Reflexive but not symmetric (c)Reflexive and transitive (d) Reflexive and symmetric but not transitive

Explain transitive relation with suitable examples.

Let R be a relation on the set of integers given by a R b :-a=2^kdotb for some integer kdot Then R is:- (a) An equivalence relation (b) Reflexive but not symmetric (c). Reflexive and transitive but not symmetric (d). Reflexive and symmetric but not transitive

A relation R_(1) is defined on RxxR rarr RxxR by (a, b)R_(1)(c, d) implies a+b+c+d is positive. How many statements S_(1), S_(2), S_(3), S_(4) are CORRECT ? S_(1) : Relation is Reflexive but not Symmetric S_(2) :, Relation is Symmetric but not Transitive S_(3) : Relation is Transitive but not Symmetric S_(4) : Relation is Equivalence