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Let A={ 1,2,3 } and R={ ( 1,2 ) ,( 1,1 ) ,( 2,3 ) } be a relat

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Let $A = {1, 2, 3}$ and $R = {(1, 2), (1, 1), (2, 3)}$ be a relation on $A$ . What minimum number of ordered pairs may be added to $R$ , so that it may become a transitive relation on $A$ ?

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Sophia Discussed

Let

A = {1, 2, 3}

and

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

be a relation on

A

. What minimum number of ordered pairs may be added to

R

, so that it may become a transitive relation on

A

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Given,

A = {1, 2, 3}

and

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

Now this relation is not transitive as

(1, 2) \in R, (2, 3) \in R

but

(1, 3) \neq \in R

So to make

R

transitive we are to add this order pair.

Then the relation will be

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

This relation

R

is transitive.

So minimum one pair is to be added to make

R

symmetric.

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Question Text	Let $A = {1, 2, 3}$ and $R = {(1, 2), (1, 1), (2, 3)}$ be a relation on $A$ . What minimum number of ordered pairs may be added to $R$ , so that it may become a transitive relation on $A$ ?
Answer Type	Text solution:1
Upvotes	150

Let A={1,2,3} and R={(1,2),(1,1),(2,3)} be a relation on A. What minimum number of ordered pairs may be added to R, so that it may become a transitive relation on A?

Text solutionVerified

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Let $A = {1, 2, 3}$ and $R = {(1, 2), (1, 1), (2, 3)}$ be a relation on $A$ . What minimum number of ordered pairs may be added to $R$ , so that it may become a transitive relation on $A$ ?