1. ## Set help appreciated

Here is the question at this link: Yfrog Image : yfrog.com/m9setsp

So here's what I've done so far: I know the A with the little hat on top means everything outside of A ie the universe. Now I know that A u B with the hat over all of that is A n B with hats over A and B only. So there's now A with 2 hats? Does that just mean A? If so, then it is A n B with a hat only over B. My answer to that is an empty set. Please help! I've done something wrong here!

2. Hello, brumby_3!

Prove that: . $\overline{\left(\,\overline{A} \cup B\right)} \cup B \;=\;A \cup B$

$\begin{array}{cccc}
1. & \overline{\left(\overlie{A} \cup B\right)} \cup B &\quad& \text{Given} \\ \\
2. & \left(\, \overline{\overline A}} \cap \overline{B}\right) \cup B &\quad& \text{DeMorgan} \\ \\
3. & \left(A \cap \overline{B}\right) \cup B &\quad & \text{Double negative} \\ \\
4. & (A \cup B) \cap (\overline{B} \cup B) &\quad& \text{Distributive} \\ \\
5. & (A \cup B) \cap U &\quad& X\cup \overline{X} \,=\,U \\ \\
6. & A \cup B &\quad& X \cap U \,=\,X
\end{array}$