On (A={1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5), and remainder (0) is not replaced by (5). Is this a binary operation on (A)?

Correct answer: Yes, because the remainder is always in (1,2,3,4)

Step 1: Check whether (ab) can be divisible by (5). Step 2: Since (5) is prime and none of (1,2,3,4) is divisible by (5), the product is not divisible by (5). So remainder (0) never occurs. Step 3: If the remainder always returns to the set, closure holds.