I'm actually a high school student but my maths teacher is kind of crazy so he decided to leave some set theory hw over the weekend, and I can't figure out these two questions. We're supposed to be looking at functions but the teacher told us we might even start group theory...

1 Show that the set of all x such that x belongs to A and x does not belong to B exists.

2 Replace the axiom of existance by the following weaker postulate:

Weak axiom of existence some set exists

Prove the Axiom of existence using the weak axiom of existence and the comprehension schema. (hint: let A be a set known to exist; consider (x belongs to A | x does not belong to x))