If the operation (a*b) on (S={0,1,2,3}) is defined as the remainder when (a+b) is divided by (4), then is this operation closed on (S)?

Correct answer: Yes because every result belongs to (S)

Step 1: For closure, (a*b) must belong to (S) for all (a,b \in S). Step 2: The remainder on division by (4) is always one of (0,1,2,3). Step 3: In exams, compare the possible remainders with the given set.