DM-Sets,Relations and Functions-Q14

+1 vote

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 in Discrete Maths by gbeditor (11,310 points)
reshown Jul 6 by gbeditor

2 Answers

+1 vote
 
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 getgatebook (29,950 points)
+1 vote
B is true mean only 2nd
answered Jul 6 by tsnikhilsharmagate2018 (18,140 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
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