PIE (Principle of Inclusion-Exclusion) A1,A2,.,AnCU<— universe 西nena=-4刘 2=1 --- ic T I≠0 Ar=∩Ai Ao=U i∈IPIE (Principle of Inclusion-Exclusion) A1, A2,...,An ￾ U universe ￾ ￾A1 ⇥ A2 ⇥ ··· An ￾ ￾ = ￾ ￾ ￾ ￾ ￾ U ￾ ⇥ n i=1 Ai ￾ ￾ ￾ ￾ ￾ AI = ￾ i￾I Ai A￾ = U = |U| ￾ ￾ I￾{1,...,n} I￾=￾ (￾1)|I|￾1 ￾ ￾ ￾ ￾ ￾ ￾ i￾I Ai ￾ ￾ ￾ ￾ ￾