Given set is {1,2,3}.

The smallest equivalence relation containing (1,2) is

{(1,1),(2,2),(3,3),(1,2),(2,1)}

Now we left with only four pairs i.e. (2,3),(3,2),(1,3),(3,1) 

Let we add one pair (2,3) then we must add (3,2) for symmetric relation. 

For transitive relation we add (1,3) and (3,1).

If we add these pairs then it is the universal relation.

So the total number of equivalence relations containing (1,2) is 2.