Q. Let R = {(2, 3), (3, 4)} be relation defined on the set of natural numbers. The minimum number of ordered pairs required to be added in R so that enlarged relation becomes an equivalence relation is :

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Solution:

We know that a relation is an equivalence relation if it is reflexive, symmetric and transitive.
For reflexive relation
For symmetric: If , then
For transitive relation:
Let and , then
Required
So minimum number of ordered pairs to be added .