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 _____________ .

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KollegeApply · Accepted Answer

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.

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