# Unions, intersections, complements, venn

• Oct 7th 2008, 05:46 PM
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
• Oct 7th 2008, 08:42 PM
Soroban

Quote:

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!

Quote:

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/////////////|          |       |  * - - - - - - - *          |       |                              |       * - - - - - - - - - - - - - - - *
• Oct 7th 2008, 11:13 PM