Question

If $A=\left\{x,y,z\right\}$, then the relation $R=\left\{\right(x,x),(y,y),(z,z),(z,x),(x,z\left)\right\}$ is:

• A. Symmetric
• B. Reflexive
• C. Transitive
• D. Equivalence

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Symmetric
B Reflexive
C Transitive
D Equivalence

$\left(i\right)$ $\left(x,x\right)\in R\forall x\in A$

So, it is reflexive

$\left(ii\right)$ since $\left(x,y\right)\in R\Rightarrow \left(y,x\right)\in R\forall x,y\in A$

So , R is symmetric

$\left(iii\right)$ since $\Rightarrow \left(x,y\right)\in R$ and $\left(y,z\right)\in R$

$\Rightarrow \left(x,y\right)\in R\forall x,y\in A$

So , it is transitive

Hence , R is an equivalence relation