Problem:
If a set $A$ has $n$ elements in it, how many reflexive relations can be defined on it?
My solution
Is the answer
summation of (n^2 - n)C(i) for i=0 to n^2 -n
$\sum_{i=0}^{n^2-n} C(n^2-n,i) = \sum_{i=0}^{n^2-n} \binom{n^2-n}i$
How?
well if i make a matrix $n\times n$ now the diagonal elements have to be selected,out of remaining $n^2-n$ any number of elements can be selected.