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 $=7$.