Question

Let $R=\left\{\right(2,3),(3,4\left)\right\}$ 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

The correct option is C $7$

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 $R=\left\{\right(2,3),(3,4),(2,2),(3,3),(2,4),(4,2),(3,2),(4,3),(4,4\left)\right\}$

So minimum number of ordered pairs to be added $=7$.