Unions, intersections, complements, venn

Printable View

October 7th 2008, 04:46 PM
pleasehelpme12345

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
October 7th 2008, 07:42 PM
Soroban

Hello, pleasehelpme12345!

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/////////////| | | * - - - - - - - * | | | * - - - - - - - - - - - - - - - *
October 7th 2008, 10:13 PM
pleasehelpme12345

Thank you ever so much! [I donated to the math forum because of you](Rofl)