Given set is A={ 1,2,3 }.
The total number of possible pairs will be,
R={ ( 1,1 ),( 1,2 ),( 1,3 ),( 2,1 ),( 2,2 ),( 2,3 ),( 3,1 ),( 3,2 ),( 3,3 ) }
For the symmetric relation in set A, if ( 1,2 )is in relation then ( 2,1 ) should also be in relation. And, ( 1,3 )is in relation then ( 3,1 ) should also be in relation.
For reflexive relation, ( 1,1 ),( 2,2 ),( 3,3 ) should be in relation.
For transitivity, if ( 1,2 )is in relation and ( 2,1 )is in relation then ( 1,1 )should be in relation.
The smallest possible equivalence containing ( 1,2 )is given by,
R 1 ={ ( 1,2 ),( 2,1 ),( 1,1 ),( 2,2 ),( 3,3 ) }
Thus, there are only two possible equivalence relations containing ( 1,2 ).
Therefore, option (B) is correct.