Hi, I need help on this problem:

Let A and B be two events. Prove the following relations by the element-wise method.

$\displaystyle (A-AB) \cup B = A \cup B $

When I say element-wise method, the idea is to show that the events on both sides of the equation are formed of the same sample point. We have to prove:

$\displaystyle (1) (A-AB) \cup B = A \cup B $

and the reverse

$\displaystyle (2) A \cup B = (A-AB) \cup B$

Any ideas?