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

Question

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

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Benjamin Discussed

Given the relation

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

on the set

A = {1, 2, 3}

, the minimum number of ordered pairs which when added to

R

to make it an equivalence relation is

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Text solutionVerified

R

is reflexive if it contains

(1, 1), (2, 2), (3, 3)

∵ (1, 2) \in R

and

(2, 3) \in R

∴ R

is symmetric if

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

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

Then,

R

is transitive is

(1, 3) \in R

Also,

(3, 1) \in R

for symmetric property.

Now,

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

Thus,

R

becomes an 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

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Question Text	Given the relation $R = {(1, 2) (2, 3)}$ on the set $A = {1, 2, 3}$ , the minimum number of ordered pairs which when added to $R$ to make it an equivalence relation is
Answer Type	Text solution:1
Upvotes	150