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

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Reflexive and symmetric

Transitive and symmetric

Equivalence

Reflexive, transitive but not symmetric.

answer is D.

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Detailed Solution

Every natural number is factor to it self, so that R is reflexiveIf (a,b) is an element of R, it means a is a factor of b, in this case b is not factor of a, so that (b,a) does not belongs to set Rso that the relation is not symmetric Suppose that (a,b), (b,c) are elements of the relation Rit means a is factor of b and b is factor of cit gives a is factor of cTherefore, (a,c) is an element of RIt implies that the relation is transitive. Hence, the relation is reflexive and transitive

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