The formula to calculate the Number of Functions is:
\[ \text{NFunctions} = (n(B))^{(n(A))} \]
The Number of Functions from Set A to Set B is the number of relations from Set A to Set B in which each element of A will be mapped with only one element in B. Number of Elements in Set B is the total count of elements present in the given finite set B. Number of Elements in Set A is the total count of elements present in the given finite set A.
Let's assume the following values:
Using the formula:
\[ \text{NFunctions} = (4)^{(3)} = 64 \]
The Number of Functions is 64.
| Number of Elements in Set A | Number of Elements in Set B | Number of Functions |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 2 | 1 |
| 0 | 3 | 1 |
| 0 | 4 | 1 |
| 0 | 5 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| 1 | 2 | 2 |
| 1 | 3 | 3 |
| 1 | 4 | 4 |
| 1 | 5 | 5 |
| 2 | 0 | 0 |
| 2 | 1 | 1 |
| 2 | 2 | 4 |
| 2 | 3 | 9 |
| 2 | 4 | 16 |
| 2 | 5 | 25 |
| 3 | 0 | 0 |
| 3 | 1 | 1 |
| 3 | 2 | 8 |
| 3 | 3 | 27 |
| 3 | 4 | 64 |
| 3 | 5 | 125 |
| 4 | 0 | 0 |
| 4 | 1 | 1 |
| 4 | 2 | 16 |
| 4 | 3 | 81 |
| 4 | 4 | 256 |
| 4 | 5 | 625 |
| 5 | 0 | 0 |
| 5 | 1 | 1 |
| 5 | 2 | 32 |
| 5 | 3 | 243 |
| 5 | 4 | 1,024 |
| 5 | 5 | 3,125 |
