# Math Help - [SOLVED] Vennn Diagram help..

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

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.) $A \cap G\subseteq F$
Fine.

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

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

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

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

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

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

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, $G\cap C=\emptyset,$ so $C\cap B\cap G=B\cap(C\cap G)=B\cap\emptyset=\emptyset\text.$ There needs to be a region that is part of all three of $B,\,C,\text{ and }G\text.$

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 $C$ covers the region for $E,$ 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..