A) Reflexive and symmetric
B) Reflexive and transitive
C) Symmetric and transitive
D) Equivalence relation
Correct Answer: B
Solution :
For any integer n, we have \[n|n\Rightarrow n\,R\,n\] So, \[n\,R\,n\]for all \[n\in Z\Rightarrow R\]is reflexive Now 2|6 but 6+2,Þ (2,6)\[\in R\]but (6, 2)\[\not{\in }R\] So, R is not symmetric. Let \[(m,n)\in R\] and \[(n,p)\in R\]. Then \[\left. \begin{align} & (m,n)\in R\Rightarrow m|n \\ & (n,p)\in R\Rightarrow n|p \\ \end{align} \right]\Rightarrow m|p\Rightarrow (m,p)\in R\] So, R is transitive. Hence, R is reflexive and transitive but it is not symmetric.
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