Hi

here's a problem I am trying to solve. Suppose A,B,C,D are sets

where is set of all functions from A to C. and is

set of all functions from B to D. Following is my work. I have already prove that

Suppose

I have also already proved that, for any sets A and B,

that means that there is a bijection from

to .

is the set of all subsets of

. But subsets of are just relations from A to C. So

is set of all relations from A to C. In similar way,

is set of all relations from B to D. Functions are special kind of relations , So

Since , there is some bijection between these two sets. Let it be h

From here on, I am stuck. We have a bijection between one family of relations to another family of relations. What we need is a bijection between the subsets of

these families.