The formula to calculate the Number of Reflexive Relations on Set A is:
\[ N_{\text{Reflexive Relations}} = 2^{n(A) \cdot (n(A) - 1)} \]
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 \( A \).
Let's assume the following value:
Using the formula:
\[ N_{\text{Reflexive Relations}} = 2^{3 \cdot (3 - 1)} = 2^{6} = 64 \]
| 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 |