# DM-Sets,Relations and Functions-Q14

Suppose that R1 and R2 are two equivalence relations on non emptydomain A then which of the following statements is true?

$\mathrm{I}$. $R1\cup R2$ is an equivalence relation

$\mathrm{I}$$\mathrm{I}$. $R1\cap R2$ is an equivalence relation

$\mathrm{I}$$\mathrm{I}$$\mathrm{I}$. $R1\oplus R2$ is an equivalence relation

Which of the following statements is true?

(A). Only $\mathrm{I}$

(B). Only $\mathrm{I}$$\mathrm{I}$

(C). Only $\mathrm{I}$$\mathrm{I}$ and $\mathrm{I}$$\mathrm{I}$$\mathrm{I}$

(D). Only $\mathrm{I}$$\mathrm{I}$$\mathrm{I}$

reshown Jul 6

$R1 \oplus R2$ is not reflexive.
Please note that $\oplus$ is symmetric difference operator.
For example Domain = {1,2,3}
R1 = {(1,1),(2,2),(3,3) }
R2= {(1,1),(2,2),(3,3),(1,2),(2,1)}

$R1 \oplus R2$ is {(1,2),(2,1) }, which is not reflexive.

answered Jul 9 by (33,170 points)