What is the possible number of reflexive relations on a set of 5 elements?
A. 2^10
B. 2^15
C. 2^20
D. 2^25

Question

Accepted Answer

2^(5^2 - 5) = 2^20. Answer: C. 2^20. A relation on an n-element set is a subset of the n^2 ordered pairs. A reflexive relation must include all n diagonal pairs (a,a). The remaining n^2 - n off-diagonal pairs can be freely included or excluded. So there are 2^(n^2 - n) reflexive relations. For n=5: 2^(25-5) = 2^20.

What is the possible number of reflexive relations on a set of 5 elements? A. 2^10 B. 2^15 C. 2^20 D. 2^25