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Math Help - Logic symbol question

  1. #1
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    Logic symbol question

    I am asked to draw a venn diagram of a few sets. But next to them there is a small C and I have no clue what that small C means.

    To see it in context look at question 6 here. Thanks so much for any help!!!

    CS2130 Assignment 1
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  2. #2
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    Re: Logic symbol question

    In this context A^c is the relative complement.
    That is U\setminus A=\{x\in U:~x\notin A\}
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  3. #3
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    Re: Logic symbol question

    so..

    6. Make a Venn diagram illustrating the case

    Ac∩Bc∩C = Ac∩B∩Cc = ∅, B ≠ C, and B ∩ C ≠ ∅.
    Few questions...

    This is supposed to be one single venn diagram.

    This is asking me to show that...
    A compliment intersect B compliment intersect C = A compliment intersect B intersect C compliment=null set?

    So is also says that B does not intersect C. So if B does not intersect C and I show Ac∩Bc∩C I end up with the area of C shading in that does not intersect A, which does not equal the null set.

    Ac∩B∩Cc for this I get the area of B shaded in that does not intersect A.


    Here is how I got it those two.

    First this means B ∩ C ≠ ∅ that B and C do not intersect.

    So my venn is circle B intersecting circle A which intersects circle C.

    So A compliment is everything outside of A.

    B compliment is everything outside of B

    Ac intersect Bc is everything outside of A and B

    and Ac intersect Bc intersect C is everywhere that is both outside of A and B and in C which ends up being the area of C not intersect by A. So I am confused at how this can = the null set.
    Last edited by ehpoc; October 4th 2011 at 03:26 PM.
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  4. #4
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    Re: Logic symbol question

    Here is the Venn diagram of A^c\cap B^c\cap C
    Attached Thumbnails Attached Thumbnails Logic symbol question-untitled.gif  
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  5. #5
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    Re: Logic symbol question

    Yes that is what I got!!! So how can that possibly =∅?????? I am confused!
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  6. #6
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    Re: Logic symbol question

    Quote Originally Posted by ehpoc View Post
    Yes that is what I got!!! So how can that possibly =∅?????? I am confused!
    Well now do the same for A^c\cap B\cap C^c.
    Do you see any overlapping?
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  7. #7
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    Re: Logic symbol question

    Ya but the question asked to show..

    Ac∩Bc∩C = Ac∩B∩Cc = ∅
    Not

    (Ac∩Bc∩C) ∩ Ac∩B∩Cc = ∅
    unless does that "=" in the middle mean intersection???
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  8. #8
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    Re: Logic symbol question

    Quote Originally Posted by ehpoc View Post
    Ya but the question asked to show..



    Not



    unless does that "=" in the middle mean intersection???
    But you are also given that B\cap C=\emptyset
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  9. #9
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    Re: Logic symbol question

    But you are also given that B\cap C=\emptyset
    Which I thought meant that B and C do not intersect anywhere.

    So Ac∩Bc∩C is...

    Logic symbol question-venn2.jpg



    and Ac∩B∩Cc is..

    Logic symbol question-venn1.jpg


    Neither of these diagrams are equal and neither = \emptyset
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