Question

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 :

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

Answer: (C)

We know that a relation is an equivalence relation if it is reflexive, symmetric and transitive.
For reflexive relation $(a, a) \in R$
For symmetric: If $(a, b) \in R$, then $(b, a) \in R$
For transitive relation:
Let $(a, b) \in R$ and $(b, c) \in R$, then $(a, c) \in R$
$\therefore $ Required $R =\{(2,3),(3,4),(2,2),(3,3),(2,4),(4,2),(3,2),(4,3),(4,4)\}$
So minimum number of ordered pairs to be added $=7$.