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Question

Given relation R={(1,2),(2,3)} on the set A={1,2,3}, the minimum number of ordered pairs which when added to

R make it an equivalence relation is


A

5

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B

6

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C

7

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D

8

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Solution

The correct option is C

7


Explanation for the correct option:

Given ,

relation R={(1,2),(2,3)} on the set

A={1,2,3}

Ris reflexive if it is contains 1,1,2,2,3,3

Therefore, 1,1R,2,3R

Therefore R is symmetric if 2,1,1,2R,

Now, R=1,1,2,2,3,3,2,1,3,2,2,3,1,2

R will be transitive if,3,1,1,3R.

Thus R becomes and equivalence Relation

by adding 1,1,2,2,3,3,2,1,3,2,(1,3),3,1.

Hence ,the total number of ordered pairs is 7.

Hence, option(C) is correct.


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