Thread: prove equal sets

I have this problem as homework, I don't think they're equal, but i need to prove it. Any body can help?
" If X and Y are sets and it is known that the collection of subsets of X equals the collection of Subsets of Y, can one conclude that X=Y?"

Originally Posted by vavi

I have this problem as homework, I don't think they're equal, but i need to prove it. Any body can help?
" If X and Y are sets and it is known that the collection of subsets of X equals the collection of Subsets of Y, can one conclude that X=Y?"

I think they are equal

My Observation: Define the set to be the union of all the singleton subsets. Now proving X=Y should be easy.