Proving a union by using the laws of algebra of sets and a new operator So I am given a new opeator A * B = complement of (A intersect B).  I apologize for not being able to post this with the correct syntax.
Using this new operator, I am to prove, algebraically, that the following is true:
(A * A) * (B * B) = A U B
I've gotten this far:

2nd part:


You are almost there! Remember De Morgan's Law: 
$${\overline {A\cap B}}={\overline {A}}\cup {\overline {B}}$$
I will use two different notations for complement so you can see it better in the next line. Continuing from what you had,
$$\overline{A} * \overline{B} = \overline{(\overline{A} \cap \overline{B})} = \overline{A^c} \cup \overline{B^c}$$
Note that the complement of the complement of a set is just that set ($\overline{A^c} = A$) and hence you have:
$$(A * A) * (B * B) = A \cup B$$
Let me know if you need further explanation!
