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Math Help - Venn Diagrams

  1. #1
    Mad
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    Venn Diagrams

    [(C n A) (B A)] n C

    Sorry it's kind of sloppy, I didn't know what to use for the symbols.

    The (B A) part has a line over it so I suppose that'd mean the complement of B A.

    The book shows a totally empty Venn Diagram with no shading. I worked out the problem, or at least thought I had, only to find that I was wrong. Why is nothing shaded?
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  2. #2
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    If (B - A) is the part of B not containing A, then I think the book is correct, because the complement of B - A (here represented by bolding) completely includes the intersection of C with A, so C n A - (B - A) is the empty set, and the intersection of C with the empty set is the empty set.
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  3. #3
    Mad
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    I still don't understand, I'm so confused.

    Can I figure this out by labeling the parts maybe? 1 through 7? And then make them into sets to see which ones A contains and then B and then C? And then work it out? I thought I saw the Prof doing that in class but I'm not sure, I was too busy trying to take notes for the deaf kids, it was my first day on the job and it was a mess.
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  4. #4
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    Hello,

    Labeling is a good idea. I use (-A) to denote the complement of A, n to denote the intersection.
    (-A)n(-B)n(-C): 0
    (-A)n(-B)nC: 1
    (-A)nBn(-C): 2
    (-A)nBnC: 3
    An(-B)n(-C): 4
    An(-B)nC: 5
    AnBn(-C): 6
    AnBnC: 7
    That is, A: 4567, B: 2367, C: 1357.
    Now, CnA: 57, B-A: 23, (-(B-A)): 14567. Omitting 14567 from 57 leaves nothing, that is, (CnA)-(-(B-A))=(emptyset). Of course, (emptyset)nC=(emptyset), confirming what icemanfan said.

    Bye.
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