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Math Help - Sets and Venn Diagram problem

  1. #1
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    Sets and Venn Diagram problem

    Illustrate [A-(B U C)] intersection [B - (A U C)] intersection [C-(A U B)] using a Venn Diagram. Explain the result by simplifying the expression analytically.

    Thanks
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  2. #2
    MHF Contributor kalagota's Avatar
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    if x \in [A - (B \cup C)], then x \in A and x \in (B \cup C)^c..

    thus, x \in A and x \in (B^c \cap C^c) and hence x \in A and x \in B^c and x \in C^c

    so if x \in [A - (B \cup C)] \cap [B - (A \cup C)] \cap [C - (A \cup B)] then x \in [A - (B \cup C)] and x \in [B - (A \cup C)] and x \in [C - (A \cup B)]

    upon "distribution", you will come up with x inside all these sets: A, B, C, A^c, B^c, C^c (which cannot happen) which will give you a conclusion that x must be in the empty set.. (But duh! something is inside the empty set!

    determine which is which in the attachment..
    Attached Thumbnails Attached Thumbnails Sets and Venn Diagram problem-illustration.gif  
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