Question

Consider the function f: Z → B (here, we use the Z instead of our "usual" A), where B = {0,1,2,3,4}, defined by f(a) = a mod 5. Compute f(0), f(2), f(27) and f(−1).

a) 0, 2, 2, -1
b) 0, 2, 2, 4
c) 0, 2, 2, 1
d) 0, 2, 2, 0

Answer 1

To compute the function f(a) = a mod 5, the remainder of each number when divided by 5 is evaluated, leading to the results: f(0) = 0, f(2) = 2, f(27) = 2, and f(−1) = 4.

Step-by-step explanation:

The student is asking to compute the values of a function f from the set of integers Z to the set B where B = {0,1,2,3,4}. The function is defined as f(a) = a mod 5. This means we need to find the remainder when each given integer is divided by 5.

• f(0) = 0 mod 5 = 0
• f(2) = 2 mod 5 = 2
• f(27) = 27 mod 5 = 2
• f(−1) = (−1) mod 5 = 4

In modular arithmetic, negative numbers are often represented by their least positive remainder. So, instead of writing f(−1) as −1, we convert −1 mod 5 into its equivalent positive remainder which is 4.