Number of Symmetric Relations on Set A Calculator

Calculate Number of Symmetric Relations



Formula

The formula to calculate the Number of Symmetric Relations on Set A is:

\[ NSymmetric Relations = 2^{\left(\frac{n(A) \cdot (n(A) + 1)}{2}\right)} \]

Definition

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 \( A \).

Example Calculation

Let's assume the following value:

Using the formula:

\[ NSymmetric Relations = 2^{\left(\frac{3 \cdot (3 + 1)}{2}\right)} = 64 \]

Conversion Chart

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