Thread: Equality Question

Why is it the case that ,

and also that

?

I'm having trouble proving these statements from the definition.

Let ... OK, now I'm lost.

Both of these statements are false. Sets are equal iff they have the same elements. The empty set does not have any elements whereas has one element . Similarly, , , , so but .

Maybe there is something in the context that would make sense of these equalities?

Thanks for the reply. I should have specified that the problems were to determine whether or not the sets were equal. Sorry for the confusion.