What is the possible number of reflexive relations on a set of 5 elements?
2018
What is the possible number of reflexive relations on a set of 5 elements?
- A.
210
- B.
215
- C.
220
- D.
225
Attempted by 86 students.
Show answer & explanation
Correct answer: C
$$\text{Total Reflexive Relations} = 2^{(n^2 - n)}$$
Calculation for 5 Elements
Given n = 5:
$$\text{Number of relations} = 2^{(5^2 - 5)}$$
$$\text{Number of relations} = 2^{(25 - 5)}$$
$$\text{Number of relations} = 2^{20}$$
Therefore, the correct choice is 3) 2^20.