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Math Help - Set Theory Problem

  1. #1
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    Set Theory Problem

    Hey everyone,
    This set theory problem has me stumped. I am not even sure what exactly I am solving for.

    These 3 Venn circles divide their union into 7 nonoverlapping regions. The number of elements in the 7 regions are 7 consecutive counting numbers. Using the same 7 consecutive counting numbers, find the differences between the maximum number of possible elements in circle A and the minimum number of possible elements in circle A.

    Circle A being the top left circle in the three circle venn diagram.
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  2. #2
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    Re: Set Theory Problem

    Quote Originally Posted by ShadowKnight8702 View Post
    These 3 Venn circles divide their union into 7 nonoverlapping regions. The number of elements in the 7 regions are 7 consecutive counting numbers. Using the same 7 consecutive counting numbers, find the differences between the maximum number of possible elements in circle A and the minimum number of possible elements in circle A.
    As I understand the setup, the seven regions contain n,~n+1,~n+2,~n+3,~n+4,~n+5,~n+6.

    The smallest number possible in set A would be n+(n+1)+(n+2)+(n+3).

    The largest number possible in set A would be (n+6)+(n+5)+(n+4)+(n+3).
    Thanks from ShadowKnight8702 and topsquark
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  3. #3
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    Re: Set Theory Problem

    Thanks Plato,
    I didn't understand the wording of the problem before, but now it makes sense. The answer is 12.
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