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 "