The probability that a randomly chosen relation from a set $A=\{1,2, \ldots n\}, n \geq 1$ to itself is a symmetric relation is

• A

  $2^{-\frac{n^2+n}{2}}$
• B

  $2^{\frac{-n^2}{2}}$
• Correct answer
  C

  $2^{\frac{n-n^2}{2}}$
• D

  $2^{\frac{n+1-n^2}{2}}$

Hence, the correct answer is option: 'C'.