The formula to calculate the Number of Relations is:
\[ \text{NRelations(A-B)} = 2^{(n(A) \cdot n(B))} \]
Number of Relations from A to B is the number of ordered pairs (a, b) where a is an element of A and b is an element of B such that \(a \in A\) and \(b \in B\), and all of which are a subset of \(A \times B\).
Let's assume the following values:
Using the formula:
\[ \text{NRelations(A-B)} = 2^{(3 \cdot 4)} = 4096 \]
| Number of Elements in Set A (n(A)) | Number of Elements in Set B (n(B)) | Number of Relations |
|---|---|---|
| 1 | 1 | 2 |
| 1 | 2 | 4 |
| 1 | 3 | 8 |
| 1 | 4 | 16 |
| 1 | 5 | 32 |
| 2 | 1 | 4 |
| 2 | 2 | 16 |
| 2 | 3 | 64 |
| 2 | 4 | 256 |
| 2 | 5 | 1,024 |
| 3 | 1 | 8 |
| 3 | 2 | 64 |
| 3 | 3 | 512 |
| 3 | 4 | 4,096 |
| 3 | 5 | 32,768 |
| 4 | 1 | 16 |
| 4 | 2 | 256 |
| 4 | 3 | 4,096 |
| 4 | 4 | 65,536 |
| 4 | 5 | 1,048,576 |
| 5 | 1 | 32 |
| 5 | 2 | 1,024 |
| 5 | 3 | 32,768 |
| 5 | 4 | 1,048,576 |
| 5 | 5 | 33,554,432 |