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Math Help - sets

  1. #1
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    sets

    A\(B ∩ C) ⊆(A\B) ∩ (A\C)
    How can I show this on a diagram?

    How can I draw a diagram for this set?
    Last edited by serhanbener; June 19th 2012 at 12:52 AM.
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  2. #2
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    Re: sets

    Quote Originally Posted by serhanbener View Post
    How can I draw a diagram for this set?
    You have two sets, not one: A \ (B ∩ C) and (A \ B) ∩ (A \ C).

    Quote Originally Posted by serhanbener View Post
    How can I show this on a diagram?
    I assume you mean Venn diagrams. Do you know how to show anything on a Venn diagram, such as the set A or B ∩ C? If not, then you need to read a textbook. If yes, then what exactly is your difficulty in drawing these slightly more complicated sets?

    I believe the inclusion you wrote is false in general. It would be true and, in fact, in would be an equality if ∩ is replaced by ∪ in the right-hand side.
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  3. #3
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    Re: sets

    Yes I know how to show anything on a Venn diagram. But I can't show the example above.
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  4. #4
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    Re: sets

    sets-venn.png

    (The picture is clickable.)

    In the left picture, B ∩ C is blue and A is red. The part of A that is just red, i.e., does not include the central purple region, is A \ (B ∩ C).

    In the right picture, A \ B is red and A \ C is blue. The purple intersection is (A \ B) ∩ (A \ C).

    You can see that the purple part in the right picture is a subset of a purely red part of the left picture, i.e., (A \ B) ∩ (A \ C) ⊆ A \ (B ∩ C). Also, the purely red part of the left picture equals the painted part of the right picture, i.e., (A \ B) ∪ (A \ C) = A \ (B ∩ C).
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  5. #5
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    Re: sets

    Many Thanks. I think there is a problem with the question."A\(B ∩ C) ⊆(A\B) ∩ (A\C)" seems to be wrong.
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