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

Question

KollegeApply · Accepted Answer

Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is reflexive, transitive but not symmetric. Explanation: Since n divides n, ∀ n ∈ N, R is reflexive. R is not symmetric since for 3, 6 ∈ N, 3 R 6 $\neq$ 6 R 3. R is transitive since for n, m, r whenever n/m and m/r $\Rightarrow$ n/r, i.e., n divides m and m divides r, then n will devide r.

AChoose Your Answer