Question

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

• A. Reflexive and symmetric
• B. Transitive and symmetric
• C. Equivalence
• D. Reflexive, transitive but not symmetric

Answer 1

The correct option is D Reflexive, transitive but not symmetric

Since n divides n, ∀ n ∈ N, R is reflexive.
R is not symmetric since $\left(3,6\right)\in R\mathrm{but}\left(6,3\right)\notin R\mathrm{as}6\mathrm{does}\mathrm{not}\mathrm{divide}3.$
R is transitive since for n, m, r whenever n/m and m/r ⇒ n/r, i.e., if n divides m and m divides r, then n will divide r.