1. [SOLVED] Vennn Diagram help..

Hi! Can anybody help me with this.. i have to make a venn diagram that satisfies the following conditions:

1.) $\displaystyle A \cap G \subseteq F$
2.) $\displaystyle B \cap E= \emptyset$
3.) $\displaystyle A \cap B= \emptyset$
4.) C-F= E
5.) $\displaystyle (D-A) \cap (C \cup F \cup B \cup G \cup E)= \emptyset$
6.) $\displaystyle C \cap B \cap G \neq \emptyset$
7.) $\displaystyle (G-F) \cap B= \emptyset$

I don't know what to do when there's subtraction involved.. I already started on the few conditions i know and it's here but i'm not sure..can anybody check it and please help me do the rest..i'll really appreciate it..

2. Originally Posted by takeyourmark
1.) $\displaystyle A \cap G\subseteq F$
Fine.

2.) $\displaystyle B \cap E= \emptyset$
$\displaystyle B$ and $\displaystyle E$ share no common elements, so draw them apart.

3.) $\displaystyle A \cap B= \emptyset$
$\displaystyle A$ and $\displaystyle B$ do not have any elements in common, so you need to get rid of the overlap.

4.) $\displaystyle C-F= E$
$\displaystyle E$ contains precisely those elements of $\displaystyle C$ which are not also in $\displaystyle F\text.$ So when you draw $\displaystyle C,\;E$ should be the portion of $\displaystyle C$ that is outside of $\displaystyle F$.

5.) $\displaystyle (D-A) \cap (C \cup F \cup B \cup G \cup E)= \emptyset$
The portion of $\displaystyle D$ that is outside of $\displaystyle A$ should not overlap $\displaystyle C,\,F,\,B,\,G,\text{ or }E\text.$

6.) $\displaystyle C \cap B \cap G\neq\emptyset$
There is some region that is common to $\displaystyle C,\,B\,\text{ and }G\text.$

7.) $\displaystyle (G-F) \cap B= \emptyset$
Okay, but you will still need to add some overlap between $\displaystyle G\text{ and }B$ to satisfy (6). This just says that that overlap must occur inside of $\displaystyle F\text.$

3. thanks Reckoner, that helped a lot! i tried to apply what you said..can you check if this is correct? Thanks again.

4. Originally Posted by takeyourmark
thanks Reckoner, that helped a lot! i tried to apply what you said..can you check if this is correct? Thanks again.
I just realized that in my above comments, I thought the D in your diagram was a B. So that explains some of what I said.

Your new attempt satisfies all but (6). In your picture, $\displaystyle G\cap C=\emptyset,$ so $\displaystyle C\cap B\cap G=B\cap(C\cap G)=B\cap\emptyset=\emptyset\text.$ There needs to be a region that is part of all three of $\displaystyle B,\,C,\text{ and }G\text.$

5. oh ok..here, i edited it..please see if it's correct..thanks for your help..

6. Originally Posted by takeyourmark
oh ok..here, i edited it..please see if it's correct..thanks for your help..
It looks like you've got it. Nice work!

One thing: You may want to make it clear that $\displaystyle C$ covers the region for $\displaystyle E,$ so that your instructor or reader isn't confused. A note should be fine.

7. Okay..Thank you very much! I couldn't have done it without your help..