I know the number of reflexive relations on a finite set is: $2^{n^{2}-n}$
The number of symmetric relations is: $2^{n+1 \choose 2} $
The number of antisymmetric relations: $2^{n}3^{n \choose 2}$
But, how do I find the number of relations that are:
non-symmetric relations on S.
number of symmetric relations which are also antisymmetric on S.
number of non-symmetric relations which are also antisymmetric on S.
