Let R be a relation on the set N of natural numbers defined by lsquo nRm n is a factor of m rsquo Th...........

Mathematics (NDA) Set theory

Let R be a relation on the set N of natural numbers defined by ‘nRm $\Leftrightarrow$ n is a factor of m’. Then, which one of the following is correct?

R is reflexive, symmetric but not transitive

R is transitive, symmetric but not reflexive

R is reflexive, transitive but not symmetric

R is an equivalence relation

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Explanation:

Given, R is a relation on the set N of natural numbers
defined by nRm $\Leftrightarrow$ n is a factor of m.
Reflexive Since, n is a factor of n for each n $\in$ N, therefore nRn, n $\forall$ N, i.e. R is reflexive.
Symmetric Note that 2 is a factor of 4 but 4 is not a factor of 2, i.e. 2R4 but 4 $\mathbb{R}$ 2 .
Thus, R is not symmetric.