What is the number of inclusive relations?

125 Views Asked by At

A binary relation on a set T is inclusive if every element in T relates to at least one element.

As an example we can say that {(2, 3), (3, 4)} is not inclusive since 4 does not relate to any element.

So, what is the number of inclusive relations on an n-set for n = 1, 2, 3 and for arbitrary n?

1

There are 1 best solutions below

8
On

HINT: An inclusive relation on $A=\{1,\ldots,n\}$ assigns to each $k\in A$ a non-empty subset of $A$. How many non-empty subsets does $A$ have?