# Math Help - Unions, intersections, complements, venn

1. ## Unions, intersections, complements, venn

Hi!

ANY help would be greatly appreciated..... I'm an art student... math is not my best subject. I'm having a very difficult time here.

So my first question:

Is ~A ∩ (B ∪ C) the same as (~A ∩ B) ∪ (~A ∩ C)???

Second question:

How would I draw this on a venn diagram-- that is to say, if I have a venn diagram labeled "A, B, and C" which part would be shaded for each of the above equations (if they are in fact not the same)?

Like I said, anything will be very helpful!

Many, many thanks

My first question:

Is . $\sim\!A \cap (B \cup C)$ the same as $(\sim\!A \cap B) \cup (\sim\!A \cap C)$ ?
Yes, it is!

Second question: How would I draw this on a Venn diagram?
We have: . $\underbrace{(\sim\!A)}_{\text{not in A}} \underbrace{\cap}_{\text{and}} \underbrace{(B \cup C)}_{\text{in B or C}}$

The Venn diagram would look like this:
Code:
      * - - - - - - - - - - - - - - - *
|                               |
|       * - - - - - - - *       |
|       | A             |       |
|       |   * - - - - - + - *   |
|       |   |           |///|   |
|   * - + - + - - - * . |///|   |
|   |///|   |       |   |///|   |
|   |///* - + - - - + - *///|   |
|   |///////|///////|/////B/|   |
|   |///////* - - - + - - - *   |
|   |/C/////////////|           |
|   * - - - - - - - *           |
|                               |
* - - - - - - - - - - - - - - - *

3. Thank you ever so much! [I donated to the math forum because of you]