Question

Mark the correct alternative in the following question:

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

विकल्प

• Reflexive and symmetric

• Transitive and symmetric

• Equivalence

• Reflexive, transitive but not symmetric

Answer 1

We have,

R = {(m, n) : n divides m; m, n ∈ N}

As, m divides m

⇒ (m, m) ∈ R ∀m ∈ N

So, R is reflexive

Since, (2, 1) ∈ R i.e. 1 divides 2

but 2 cannot divide 1 i.e. (2, 1) ∉ R

So, R is not symmetric

Let (m, n) ∈ R and (n, p) ∈ R.

Then, n divides m and p divides n

⇒ p divides m

⇒ (m, p) ∈ R

So, R is transitive

Hence, R is Reflexive, transitive but not symmetric.