# DM-Sets,Relations and Functions-Q14

+2 votes

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}$

asked Jul 5
reshown Jul 6

## 2 Answers

+2 votes

Best answer

$R1 \oplus R2$ 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)
0 votes
B is true mean only 2nd
answered Jul 6 by (31,640 points)
what is the III option , is that XOR, how can XOR be applied on relations?
(A U B)-( A n B) here n is intersection
A U B is not equ and intersection is equ but when we sub a int b from a U b than reflexive property break.
XOR is nothing but symmetric difference
Answer: