Let R ={(2,3),(3,4)} be a relation defined on the set A {1,2,3,4} the minimum number of ordered pairs required to be added in R . so that enlarged relation becomes an equivalance relation is________________

The given relation is $R=\left\{\left(2,3\right),\left(3,4\right)\right\}$  and the given set  is $A=\left\{1,2,3,4\right\}$
To make it reflexive, add the ordered pairs $\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right)$

The enlarge R is $R=\left\{\right(\mathrm{1,1}\left)\right(\mathrm{2,2}),(\mathrm{3,3}),(\mathrm{4,4}),(\mathrm{2,3}),(\mathrm{3,4}\left)\right\}$

To make it symmetric relation add $\left(3,2\right),\left(4,3\right)$

The enlarge R is $R=\left\{\right(\mathrm{1,1}\left)\right(\mathrm{2,2}),(\mathrm{3,3}),(\mathrm{4,4}),(\mathrm{2,3}),(\mathrm{3,4}),(\mathrm{3,2}),(\mathrm{4,3}\left)\right\}$

This is symmetric and transitive also

Therefore, the enlarge R is equivalence relation.

Hence, to make the given relation R equaivalence relation, add$\boxed{\mathbf{6}}$ ordered pairs