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JEE Main & Advanced Mathematics Sets Question Bank Relations

  • question_answer
    In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y)| x, y \[\in \] A and x < y}. Then R is

    A) Reflexive

    B) Symmetric

    C) Transitive

    D) None of these

    Correct Answer: C

    Solution :

    Since\[x\not{<}x,\] therefore R is not reflexive. Also \[x<y\] does not imply that \[y<x,\]So R is not symmetric. Let \[x\text{ }R\,y\]and\[y\,R\,z\]. Then, \[x<y\]and \[y<z\] Þ \[(a,b)\in R\] i.e., \[x\,R\,z\]. Hence R is transitive.


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