JEE Main & Advanced Mathematics Sets Question Bank Critical Thinking

  • question_answer Let R be a relation on the set N be defined by {(x, y)| x, y  \[\overset{\hat{\ }}{\mathop{i}}\,\] N, 2x + y = 41}. Then R is

    A) Reflexive

    B) Symmetric

    C) Transitive

    D) None of these

    Correct Answer: D

    Solution :

    On the set N of natural numbers, \[R=\{(x,y):x,y\in N,2x+y=41\}\]. Since \[(1,1)\notin R\]as \[2.1+1=3\ne 41\]. So, R is not reflexive. \[(1,\,39)\in R\]but \[(39,\,1)\notin R\]. So R is not symmetric (20, 1) (1, 39 \[\in R\]. But \[(20,39)\notin R\], So R is not transitive.

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