Number of relations possible on a set with N elemets

Let N be the number of elements in the set and below table gives number of relations possible for respective property

Relation	Number of relations possible
Reflexive	2^{N^2-N}
Symmetric	2^N(N+1)/2
Anti-Symmetric	2^N * 3 ^N(N-1)/2
Asymmetric	3 ^N(N-1)/2
Irreflexive	2^{N^2-N}

For the proofs you can check this url

http://gateoverflow.in/3123/elements-many-relations-there-irreflexive-antisymmetric

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