1. ## Simplifying sets, I need advice

I tried to simplify it as much as I could. Its my first week in this course and it's mind breaking. Here is what I got. If I have done it wrong can you please reply and let me know where I am wrong at? Thank you so much!
______
(A - B) U A = (Ᾱ U B) U A = (Ᾱ∩A) U B = Ø U B = B

____
(A-B) U A= B

2. I don't know how you went from the second to third step. There is no intersection in the second, and suddenly there is one in the third.

Union is associative. and commutative. The union of A with its complement is the whole space X. The union of X with any set B is still X. So the answer is X.

Drawing a simple Venn diagram first will show you what you're trying to get as your answer.

3. Dr Steve, So would it look more like this?

(Ᾱ U A) U B = Ø U B = B I am so confused in this course that I don't even know where to start with the Venn Diagram and my instructor is not a bit helpful.

When you state X do you mean Ø ?

4. No. $\emptyset$ is the empty set. This set has no elements. I assume (but I could be wrong - I don't know what you were doing prior to this example) that here you're considering A and B to be subsets of some set X. So, by X, I mean "everything".

So $X\cup B=X$.

5. Hello, compstudent!

Your mixing a number of concepts . . .

$\text{Simplify: }\;(\overline{A - B}) \cup A$

$\begin{array}{cccccc}
(\overline{A - B}) \cup A && \text{Given} \\ \\[-3mm]
(\overline{A \cap \overline{B}}) \cup A && \text{d{e}f. Subtr'n} \\ \\[-3mm]
(\overline{A} \cup \overline{\overline {B}}) \cup A && \text{DeMorgan} \\ \\[-3mm]
(\overline{A} \cup B) \cup A && \text{dbl. negative} \\ \\[-3mm]
\overline{A} \cup (B \cup A) && \text{Associative} \\ \\[-3mm]
\overline{A} \cup (A\cup B) && \text{Commutative} \\ \\[-3mm]
(\overline{A} \cup A) \cup B && \text{Associative} \\ \\[-3mm]
U \cup A && S \cup \overline{S} \,=\,U \\ \\[-3mm]
U && U \cup S \,=\,U \end{array}$

6. Thank you both of you Dr. Steve and Soroban You both have helped me out sooo much! Soroban: your format helped me out the most. Thank you!!!