Question

Number of irreflexive relation

Answer 1

Total no of relation for set {1,2,3 .............n} =$n^{2}$

as we know irreflexive relation never be include diagonal element like (1,1),(2,2)......(n,n)

(1,1)(2,2)(3,3)...............(n,n) (1,2)(2,1),(1,3)(3,1)...............  

so total here $n^{2}$ relation in which i exclude 'n' diagonal elements.

So remaining element will be= $n^{2-n}$  

for each element we have two choice either take or don't take so

Total no of irreflexive relation is=$2^{n^{2}-n}$ .