Q.

Let R be a relation on the set N of natural numbers defined by nRm⇔n is a factor of m (i.e., n\m). Then R is

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a

Reflexive and symmetric

b

Transitive and symmetric

c

Equivalence

d

Reflexive, transitive but not symmetric

answer is D.

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Detailed Solution

Since n\n for all n∈N, therefore R is reflexive. Since 26 but 6/2, therefore R is not symmetric.Let n R m and mRp⇒nm and mp⇒n|p⇒nRp. So, R is transtive.
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