4.5 Inclusion-Exclusion principle and applications 4.5.1 Inclusion-Exclusion principle Theorem 4.3: Leta and b be finite sets. Then A∪B|=4|+|B|A∩B| Proof: Because a∪B=A∪(B-A),andA∩(B A)=O, by theorem we obtain AU BA+B-Al B-A=? Theorem 4.14: Let a1,a2,,,An be finite sets. Then ∪4∑A|-∑A∩4|+…+(-1)”1A∩4n…∩A i=14.5 Inclusion-Exclusion principle and Applications ▪ 4.5.1 Inclusion-Exclusion principle ▪ Theorem 4.13：Let A and B be finite sets. Then |A∪B|=|A|+|B|-|A∩B|。 ▪ Proof：Because A∪B=A∪(B-A)，and A∩(B￾A)=,by theorem we obtain |A∪B|=|A|+|B-A|. ▪ |B-A|=？ ▪ Theorem 4.14：Let A1 ,A2 ,…,An be finite sets. Then | | | | | | ( 1) | | 1 2 1 1 1 n n i j i j n i i n i Ai A A  A  A  A  A − = =  = − + + −