• # 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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