PIE (Principle of Inclusion-Exclusion) A1,A2,...,An CU<universe rena。女-4 i=1 -叫￡H门 IC{1,,n} AI=∩A 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} (￾1)|I|￾1 ￾ ￾ ￾ ￾ ￾ ⇤ i⇤I Ai ￾ ￾ ￾ ￾ ￾