Question

Let X = {1, 2, 3, 4, 5} and Y = {u, v,w, x, y}, and define h: X → Y as follows:

h(1) = v, h(2) = x, h(3) = v, h(4) = v, h(5) = y.

Draw an arrow diagram for h.

Answer 1

The arrow diagram for h is as follows:

1 → v

2 → x

3 → v

4 → v

5 → y

Step-by-step explanation:

In this question, we are given two sets X and Y and a function h that maps elements from X to Y. The function h is defined as h(1) = v, h(2) = x, h(3) = v, h(4) = v, h(5) = y. This means that the element 1 in set X is mapped to element v in set Y, element 2 is mapped to x, element 3 is mapped to v, element 4 is mapped to v, and element 5 is mapped to y.

To represent this function h visually, we can use an arrow diagram. In an arrow diagram, each element from the domain (set X) is represented by an arrow pointing to its corresponding element in the co-domain (set Y). In this case, we have five arrows representing the five elements in set X, with their respective elements in set Y written on the other end of the arrow.

In the first step, we can see that element 1 in set X is mapped to element v in set Y. Similarly, element 2 is mapped to x, element 3 is mapped to v, element 4 is mapped to v, and element 5 is mapped to y. This completes the arrow diagram for function h.

In summary, the function h maps elements from set X to set Y by assigning a specific element from set Y to each element in set X. The arrow diagram helps us visualize this mapping in a clear and organized manner.