Question

Exercise 2

A function f {1,2,3,4,5} {0, 1,2,3,4} is defined by the rule: f(n) is the remainder after 3n is
divided by 5. Draw an arrow diagram for this function. Hence state whether is one-to-one and
whether f is onto.

Answer 1

The arrow diagram is attached

Since, for each value of n, there is only one value of f(n) the function is one-to-one

Step-by-step explanation:

We are given f(n) = remainder of 3n/5

Let's compute the values of the remainder for each of the n values {1, 2, 3, 4, 5}

n 3n/5 Quotient Remainder
1 3/5 0 3

2 6/5 1 1

3 9/5 1 4

4 12/5 2 2

5 15/5 3 0