An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is:

Question

An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is: (A) reflexive and symmetric (B) reflexive and transitive (C) symmetric and transitive (D) equivalence relation

Tardigrade Admin · Accepted Answer

For any integer n, we have (n/n) ⇒ n Rn ∴ nRn ∀ n ∈ Z ⇒ R is reflexive. and for any integers m, n and p, we have (m/n) and (n/p) ⇒ m Rn and nRp ∴ mRp ∀ m ,n , p ∈ Z ⇒ R is transitive.

Q. An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is:

reflexive and symmetric

reflexive and transitive

symmetric and transitive

equivalence relation

For any integer n, we have $\frac{n}{n} \Rightarrow n R n$
$∴ n R n \forall n \in Z \Rightarrow R$ is reflexive.
and for any integers m, n and p, we have
$\frac{m}{n}$ and $\frac{n}{p} \Rightarrow m R n$ and $n Rp$
$∴ m Rp \forall m, n, p \in Z \Rightarrow R$ is transitive.