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How can I apply the inclusion exclusion principle when I have $$|Q|+|P|+|R|-|Q\cup P| -|Q\cup R|-|P\cup R|+|Q\cap P\cap R|$$

I'm not sure how to convert the unions into intersections here $$"|Q\cup P| -|Q\cup R|-|P\cup R|"$$ so that I can apply the inclusion exclusion principle.

Adam Rubinson
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Kaia Zhai
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  • Well... With the inclusion-exclusion principle. –  May 04 '21 at 06:46
  • Though looking at this thing I'm not exactly sure what the goal is. –  May 04 '21 at 06:49
  • I believe all those unions are actually supposed to be intersections. – Greg Martin May 04 '21 at 07:01
  • Yes, the problem is that all the unions are supposed to be intersections. However, all the unions are currently right now unions and I'm not sure how to convert them into intersections. – Kaia Zhai May 04 '21 at 07:02
  • "how to convert them into intersections" Using the inclusion exclusion principle, of course. But you forgot to state what the actual goal of the exercise is. – dxiv May 04 '21 at 07:05
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    Please provide an actual problem statement. It is unclear what the problem or goal is here. – Christoph May 04 '21 at 07:05
  • This looks like an expansion of $n(P \cup Q \cup R) $. Drawing a Venn Diagram should help, as well as using the formula for the (number of elements in) union of two sets, $\ n(A\cup B) = n(A) + n(B) - n(A \cap B)$. – Adam Rubinson May 04 '21 at 07:15

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