# Set Theory Problem

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• September 26th 2013, 07:40 AM
ShadowKnight8702
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.
• September 26th 2013, 08:14 AM
Plato
Re: Set Theory Problem
Quote:

Originally Posted by ShadowKnight8702
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 $(n+6)+(n+5)+(n+4)+(n+3)$.
• September 26th 2013, 08:40 AM
ShadowKnight8702
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.