Combinatorics

Let a nz 1 n 300 3n b nz

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Unformatted text preview:   Theorem: Let A1,A2, …,An be finite sets, then |A1∪ A2 ∪...∪An|= Σi|Ai| - Σi<j|Ai ∩ Aj| + Σi<j<k|Ai ∩ Aj ∩ Ak| - … +(- 1)n+1 |A1∩A2∩...∩An| Each summa5on is over •  all i, •  pairs i,j with i<j, •  triples with i<j<k, etc. CSCE 235 Combinatorics 9 PIE Theorem: Example 1 •  To illustrate, when n=3, we have |A1∪ A2 ∪A3|= |A1|+ |A2| +|A3| - [|A1∩A2|+|A1∩A3|+|A2∩A3|] +|A1 ∩ A2 ∩ A3|...
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