First slide

Relations XII

Question

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

Easy

A

Reflexive and symmetric
B

Reflexive and transitive
C

Symmetric and transitive
D

Equivalence relation

Solution

For any integer n, we have $n | n \Rightarrow nRn$
So, $nRn$ for all $n \in Z \Rightarrow R$ is reflexive
Now $2 | 6$ but $6 + 2 \Rightarrow (2, 6) \in R but (6, 2) \notin R$
So, R is not symmetric.
Let $(m, n) \in R and (n, p) \in R .$
Then $(m, n) \in R \Rightarrow m | n \Rightarrow m | p \Rightarrow (m, p) \in R (n, p) \in R \Rightarrow n | p$
So, R is transitive.
Hence, R is reflexive and transitive but it is not symmetric.

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