For this question, we are allowed to assume the following is true and has been proven:

Let A,B R and p R. Prove that p is an accumulation point of A B if and only if p is an accumulation point of A or p is an accumulation point of B: (A B)'=A' B'.

Now since we assumed the above is true,

Conclude that the closure of a union is the union of the closures:

(A B)^cl=A^cl B^cl. How would I go about proving this?