DM - Functions & Relations -Q11

+1 vote

Suppose that R1 and R2 are two equivalence relations on non empty set A then which of the following statements is necessarily 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 Jun 24 in Discrete Maths by gbeditor (44,490 points)
reshown 6 days ago by gbeditor

1 Answer

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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 4 days ago by deepak-gatebook (112,390 points)
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