12th Class Mathematics Relations and Functions

  • question_answer 4)
    Show that the relation R defined as R = {(a, b) : a  b} is reflexive and transitive   but not symmetric.          

    Answer:

          R = {(a, b) : a  b, a, b R } Reflexive : As a  a  a      (a, a)  a  R is reflexive. Symmetric : As 1, 2 and 1  2 (1, 2) But is not symmetric. Transitive : (a, b)  and (b, c) a, b,c  and  R is transitive. Hence R is reflexive and transitive but not symmetric.  


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