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

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

Then, the ordered pair to be added to R to make it the smallest equivalence relation is:

Question

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

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

Then, the ordered pair to be added to R to make it the smallest equivalence relation is:

Smart Achievers · Accepted Answer

(2)

Ans. (3, 1)

Explanation:

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

$\Rightarrow R is reflexive.$

$(1, 3) \in R$

$(1, 3) \in R but (3, 1) \notin R$

$\Rightarrow R is not symmetric.$

To make $R$ an equivalence relation, we can add (3, 1).

Clearly, $R$ is reflexive and transitive. For $R$ to be symmetric, we should add (3, 1) in R.

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