The formula to calculate the Number of Symmetric Relations on Set A is:
\[ NSymmetric Relations = 2^{\left(\frac{n(A) \cdot (n(A) + 1)}{2}\right)} \]
The Number of Symmetric Relations on Set A is the number of binary relations \( R \) on a set \( A \) which are symmetric, meaning for all \( x \) and \( y \) in \( A \), if \( (x,y) \in R \), then \( (y,x) \in R \). The Number of Elements in Set A is the total count of elements present in the given finite set \( A \).
Let's assume the following value:
Using the formula:
\[ NSymmetric Relations = 2^{\left(\frac{3 \cdot (3 + 1)}{2}\right)} = 64 \]
| Number of Elements in Set A (n(A)) | Number of Symmetric Relations |
|---|---|
| 1 | 2.000000000000 |
| 2 | 8.000000000000 |
| 3 | 64.000000000000 |
| 4 | 1,024.000000000000 |
| 5 | 32,768.000000000000 |