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JEE Main & Advanced Sample Paper JEE Main Sample Paper-32

  • question_answer
    The relation P defined from R to R as \[a\,\,p\,\,b\,\,\Leftrightarrow 1+ab>0,\], for alia, be R is

    A) reflexive only

    B) reflexive and symmetric only

    C) transitive only                     

    D) equivalence     

    Correct Answer: B

    Solution :

    For every (a, a)                 \[\Rightarrow \,1+{{a}^{2}}\,>0,\]where\[a\in R\]. \[\therefore \]Relation is reflexive. Also if \[(a,b)\Rightarrow \,1+ab>0\] Then (b, a) will also satisfy \[1+ba>0.\] \[\therefore \]Relation is symmetric also. But \[\left( 1,\frac{-1}{2} \right)\in P,\left( \frac{-1}{2},-10 \right)\in P\] and \[(1,-10)\notin P.\] \[\Rightarrow \]Relation is not transitive.


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