Number of Reflexive Relations on Set A Calculator

Calculate Number of Reflexive Relations on Set A



Formula

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

\[ N_{\text{Reflexive Relations}} = 2^{n(A) \cdot (n(A) - 1)} \]

Definition

Number of Reflexive Relations on Set A is the number of binary relations \( R \) on a set \( A \) in which all the elements are mapped to themselves, which means for all \( x \in A \), \( (x,x) \in R \). 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:

\[ N_{\text{Reflexive Relations}} = 2^{3 \cdot (3 - 1)} = 2^{6} = 64 \]

Conversion Chart

Number of Elements in Set A (n(A)) Number of Reflexive Relations on Set A
1 1
2 4
3 64
4 4,096
5 1,048,576