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Math Help - [SOLVED] Vennn Diagram help..

  1. #1
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    [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..
    Attached Thumbnails Attached Thumbnails [SOLVED] Vennn Diagram help..-venn.bmp  
    Last edited by takeyourmark; February 14th 2009 at 07:47 AM.
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  2. #2
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    Quote Originally Posted by takeyourmark View Post
    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.
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    thanks Reckoner, that helped a lot! i tried to apply what you said..can you check if this is correct? Thanks again.
    Attached Thumbnails Attached Thumbnails [SOLVED] Vennn Diagram help..-venn.bmp  
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    Quote Originally Posted by takeyourmark View Post
    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.
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    oh ok..here, i edited it..please see if it's correct..thanks for your help..
    Attached Thumbnails Attached Thumbnails [SOLVED] Vennn Diagram help..-venn.bmp  
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    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by takeyourmark View Post
    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.
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    Okay..Thank you very much! I couldn't have done it without your help..
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