Let `R` be a relation on the set `N` of natural numbers defined by `n\ R\ m` if `n` divides `m`. Then, `R` is

Options

A. Reflexive and Symmetric
B. Symmetric and Transitive
C. Equivalence
D. Reflexive and Transitive but not Symmetric

Answer

D

Explanation

Let there be a natural number `n`,

We know that n divides `n,` which implies nRn.

So, Every natural number is related to itself in relation R.

Thus relation R is reflexive .


Let there be three natural number `a,b,c` and let `aRb,bRc`

`aRb` implies `a` divides `b` and `bRc` implies `b` divides `c`,
which combinedly implies that a divides c i.e. aRc.

So, Relation R is also transitive
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