Question

The number of reflexive relations on a set \( A \) of \( n \) elements is equal to:

• A. \( 2^{n^2} \)
• B. \( n^2 \)
• C. \( 2^{n(n-1)} \)
• D. \( n^2 - n \)

Hint:

For relation counting problems: Total relations on \( n \) elements = \( 2^{n^2} \) Reflexive relations = Fix diagonal pairs, vary rest Formula to remember: \( 2^{n^2-n} \)

Answer 1

The Correct Option is C