Let \( A = \{1, 2, 3\} \). The number of equivalence relations containing \( (1, 2) \) and \( (2, 1) \) is:

For reflexivity, \( (1,1), (2,2), (3,3) \) must be present. Given \( (1,2) \) and \( (2,1) \), symmetry is satisfied. For transitivity, we can either have no other pairs (giving the equivalence classes \( \{1,2\}, \{3\} \)) or include all pairs (universal relation). Thus, exactly 2 equivalence relations.