Hi, I have the following problem. I have solved the second part, but I don't know how to solve the first one.

Let be the set of all odd cardinality subsets of the set , and let be the set of all even cardinality subsets of the set . Do the following:

- Find a bijection ,

- Express and in terms of the number .

So the part I don't know is the first one, but here is what I got for the second one. Is it OK? And do you know a bijection for the first part? Thanks!

"There is a bijection between and because .

Also, we know that if , we have and . But we also know that in every set , we only have odd and even subsets, so if then we can say

, so and "