JEE Main & Advanced Mathematics Set Theory and Relations Question Bank Critical Thinking

  • question_answer Let R be a relation on the set N of natural numbers defined by nRm \[\Leftrightarrow \] n is a factor of m (i.e., n|m). Then R is

    A) Reflexive and symmetric

    B) Transitive and symmetric

    C) Equivalence

    D) Reflexive, transitive but not symmetric

    Correct Answer: D

    Solution :

    Since n | n for all \[n\in N\], therefore R is reflexive. Since 2 | 6 but \[6\not{|}2\], therefore R is not symmetric. Let n R m and m R p Þ n|m and m|p Þ n|p Þ nRp. So, R is transitive.

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