As the title says, I'm trying to solve the following problem:
Suppose $X$ is a set all of whose elements are finite sets. Prove that there is a set $Y$ consisting of all the elements of $X$ that have an even number of elements.
I'm working in ZF, and assuming only the Empty Set Axiom, the Axioms of Extensionality, Pairs, Unions and the Comprehension Scheme.
The question specifies I can't use the Power Set Axiom, but I have separately proven that in the case where $X$ is a finite set then there is a set which is its powerset, and so can use this fact.
I haven't really come up with any ideas of where to go, so would appreciate any help you could offer.