Let a nz 1 n 300 3n b nz

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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|...
View Full Document

Ask a homework question - tutors are online