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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 43

  • question_answer
    Let W denote the words in the English dictionary. Define the relation R = { \[(x,y)\in W\times W:\] as  the words x and y have at least one letter in common}. Then R is

    A) Not reflexive, symmetric and transitive 

    B) Reflexive, symmetric and not transitive

    C) Reflexive, symmetric and transitive                    

    D) Reflexive, not symmetric and transitive

    Correct Answer: B

    Solution :

    [b] Clearly, \[\left( x,x \right)\in R\,\forall \,x\in W\]. So, R is reflexive. Let \[\left( x,y \right)\in R,\] then \[\left( y,x \right)\in R\] as x and y have at least one letter in common. So, R is symmetric. But R is not transitive as common alphabet between words x and y and that between y and z may not be the same.


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