Give a relation R={(1,2), (2,3)} on the set of natural numbers, add a minimum number of ordered pairs.

$R=\{(1,2),(2,3)\}$

A)To make the relation symmetric, we have to add (2,1) and (3,2) in R. 
Enlarged symmetric relation $R^{\prime }=\{(1,2),(2,3),(2,1),(3,2)\}$

B) To make enlarged relation transitive , we have to add (1,3), (1,1),(2,2) in R'.
Also, we need to add (3,1) to make it symmetric
So, the new enlarged relation is $R^{\prime \prime }=\{(1,2),(2,3),(2,1),(3,2),(1,1),(2,2),(3,1)\}$ 

C) For enlarged relation to be symmetric, we need to add (1,1) in R''
$R^{\prime \prime }=\{(1,2),(2,3),(2,1),(3,2),(1,1),(2,2),(3,1),(1,1)\}$ 

D) For enlarged relation to be equivalence,