On (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{3}). What are the distinct equivalence classes of this relation?

Correct answer: ({1,4},{2,5},{3,6})

Step 1: Numbers with the same remainder on division by (3) belong to the same class. Step 2: Remainder (1) gives ({1,4}), remainder (2) gives ({2,5}), and remainder (0) gives ({3,6}). Step 3: Equivalence classes are disjoint and together cover the whole set.