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For the set A={ 1,2,3 } , define a relation R on the set A as

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For the set $A = {1, 2, 3}$ , define a relation $R$ on the set $A$ as follows:
$R = {(1, 1), (2, 2), (3, 3), (1, 3)}$
Write the ordered pairs to added to $R$ to make the smallest equivalence relation.

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Sophia Discussed

For the set

A = {1, 2, 3}

, define a relation

R

on the set

A

as follows:

R = {(1, 1), (2, 2), (3, 3), (1, 3)}

Write the ordered pairs to added to

R

to make the smallest equivalence relation.

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Text solutionVerified

It is clearly evident that R is a reflexive relation and also a transitive relation ,

but it is not symmetric as (1,3) is present in R but (3,1) is not present in R .

So, To make R an equivalence relation we can simply add (3,1) to R which will also not disturb transitivity and reflexivity .

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Question Text	For the set $A = {1, 2, 3}$ , define a relation $R$ on the set $A$ as follows: $R = {(1, 1), (2, 2), (3, 3), (1, 3)}$ Write the ordered pairs to added to $R$ to make the smallest equivalence relation.
Answer Type	Text solution:1
Upvotes	150