# True or False: An integer m is said to be related to another integer n if m is a integral multiple of n.This relation in Z is reflexive,symmetric and transitive.

Toolbox:
• A relation R in a set A is called $\mathbf{ reflexive},$ if $(a,a) \in R\;$ for every $\; a\in\;A$
• A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
• A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$
Given : m,n are integer z
Relation R defined by
m R n if m is a integral multiple of n
Let mRm m is integral multiple of m itself
Therefore R is reflexive
Let $m R n$
=> m is integral multiple of n
$=>m=pn\qquad where \;p \in Z$
$=> n=\frac{1}{p} m$
$\frac {1}{p} \notin z \;for \;all\;p \in z$
Therefore n is not integral mutiple of m
mRn does not imply n R m
R is not symmetric
Solution: Hence the given statment is 'False'

edited Mar 28, 2013 by meena.p