If (f:\mathbb{Z}\to{0,1,2}) is defined such that (f(n)) is the remainder when (n) is divided by (3), what type of function is (f)?

Correct answer: Onto but not one-one

Step 1: When an integer is divided by (3), the remainder is one of (0,1,2). Step 2: All three remainders are obtained, for example (f(3)=0), (f(4)=1), and (f(5)=2). Hence the function is onto. But many integers give the same remainder, so it is not one-one. Step 3: In remainder-based questions, list all possible remainders.