Why does finding the union of these three sets yield a negative number?I've been working on a homework problem that I can't seem to be able to solve.The question states:Suppose 25 people attended a conference that contains 3 sessions. 15 people attended session #1; 18 people attended session #2; 12 people attended session #3. At least how many people attended all 3? u , sin ⁡ 2 u = − 2 sin ⁡ u cos ⁡ uHowever, when I'm applying this problem to 3 sets, I obtained a negative number.I computed the result: |A∪B∪C| ≤ 5 where |A∩B| ≥ 8, |A∩C| ≥ 2, |B∩C| ≥ 5, however, I don't quite understand the negative part where 25 ≥ |(A∩B)∪C| = |A∩B| + |C| - |A∩B∩C| (shorter way to find the minimum). The result just ends up as |A∩B∩C| + 25 ≥ 20 which would result in a negative unless I can somehow divide both sides by -1 which would change the equality?

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Why does finding the union of these three sets yield a negative number?I&#039;ve been working on a homework problem that I can&#039;t seem to be able to solve.The question states:Suppose 25 people attended a conference that contains 3 sessions. 15 people attended session #1; 18 people attended session #2; 12 people attended session #3. At least how many people attended all 3?  u  ,  sin  ⁡  2  u  =  −  2  sin  ⁡  u  cos  ⁡  uHowever, when I&#039;m applying this problem to 3 sets, I obtained a negative number.I computed the result: |A∪B∪C| ≤ 5 where |A∩B| ≥ 8, |A∩C| ≥ 2, |B∩C| ≥ 5, however, I don&#039;t quite understand the negative part where 25 ≥ |(A∩B)∪C| = |A∩B| + |C| - |A∩B∩C| (shorter way to find the minimum). The result just ends up as |A∩B∩C| + 25 ≥ 20 which would result in a negative unless I can somehow divide both sides by -1 which would change the equality?

Daniel Valdez · Accepted Answer

Why do you set   P  (  A  ∪  B  )  =  100  %?All you know is   P  (  A  ∪  B  ∪  C  )  =  100  %  ,  P  (  A  )  =  60  %  ,  P  (  B  )  =  72  %, and   P  (  C  )  =  48  %You will not be able to compute any of   P  (  A  ∩  B  )  ,  P  (  A  ∪  B  )  ,  P  (  A  ∩  C  )  ,  P  (  A  ∪  C  )  ,  P  (  B  ∩  C  )  , and   P  (  B  ∪  C  )  .And in fact you also cannot know   P  (  A  ∩  B  ∩  C  ).Nevertheless, how can you minimize   P  (  A  ∩  B  ∩  C  )? That is the question. Use your inclusion-exclusion formula to figure that out.And by the way, there is no need to convert to probabilities/percentages here ... you can just work with the raw numbers if you use the formula:  |  A  ∪  B  ∪  C  |  =  |  A  |  +  |  B  |  +  |  C  |  −  |  A  ∩  B  |  −  |  A  ∩  C  |  −  |  B  ∩  C  |  +  |  A  ∩  B  ∩  C  |

Why does finding the union of these three sets yield a negative number? I've been working on a home

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