Set Theory Question

Question

Let's say I have a question like this:

I have 3 different groups A, B and C and now I'm given the percentages of how many people are in each group. There can also be people in 2 groups or in all three groups and I have information about the number of people who are in two groups. If the question ask how many people are in all groups, I can use the following formula:

100 = A + B + C –   –

But my question is why do you have to subtract the number of people in all three groups twice? Can anybody elaborate on that please?

Bunuel · Answer

The following post addresses exactly the question you have: formulae-for-3-overlapping-sets-69014.html#p729340 Hope it helps.

BN1989 · Answer

Yes it does. Thanks a lot.

fxsunny · Answer

Let's say you had two intersecting sets...A and B; and you would like to calculate  A union B .

How would you do it?  
..... A + B - (A intersection B). Right?

Now, ask yourself why did you subtract (A intersection B) just once? 
... because when you added A and B, the common element (A intersection B) got counted twice. You needed it just once, so you subtracted it once.

Applying the same logic, to three sets:
When you calculate   by adding A + B + C, the (A intersection B intersection C) piece gets counted three times. You need it accounted for just once, so you subtract it twice.

Makes sense?

Set Theory Question

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