If (R) on (A={1,2,3}) is reflexive and symmetric and ((1,2),(2,3)\in R), which pair is necessary to make (R) an equivalence relation?

Correct answer: ((1,3))

Step 1: Equivalence also requires transitivity. Step 2: ((1,2)) and ((2,3)) require ((1,3)). Step 3: Reflexivity gives self-pairs, but this third pair comes from transitivity.