PIE (Principle of Inclusion-Exclusion) A1,A2,...,An CU universe 元nn周-U4 -2,-y-1QA I{1，，n} I≠0 A虹=∩A, Ao=U i∈I PIE (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 ￾ ￾ ￾ ￾ ￾