On (A={1,2,3,4,5,6}), (aRb) if (a) and (b) leave the same remainder on division by (3). Choose the correct option for (R).

Correct answer: It is transitive

Step 1: If (a) and (b) have the same remainder, and (b) and (c) have the same remainder, then all three have the same remainder. Step 2: So (a) and (c) also have the same remainder, meaning ((a,c)\in R). Step 3: Such relations can be checked quickly by forming remainder classes.