Which single pair should be added to R={(1,1),(2,2),(3,3),(1,2)} so that it becomes an equivalence relation on A={1,2,3}?

Correct answer: (2,1)

The correct answer is A, (2,1). The relation already contains (1,1), (2,2), and (3,3), so it is reflexive. The pair (1,2) is present, and symmetry therefore requires its reverse, (2,1). After adding that pair, the relation contains all ordered pairs within the class {1,2}, together with (3,3). It is transitive: links between 1 and 2 stay inside {1,2}, and 3 is related only to itself. Thus the equivalence classes are {1,2} and {3}. B, C, and D would connect 3 with another element, but adding only one such pair would either violate symmetry or create further requirements, so they cannot produce an equivalence relation by themselves. Memory cue: equivalence classes behave like complete internally connected groups; an existing one-way link needs its reverse.