PIE (Principle of Inclusion-Exclusion) A1,A2,...,An CU<universe AnA2n…An=∑(-1)I|A IC{1,,n} A1=∩Ai Ao=U i∈IPIE (Principle of Inclusion-Exclusion) A1, A2,...,An ￾ U universe ￾ ￾A1 ⇥ A2 ⇥ ··· An ￾ ￾ = AI = ￾ i￾I Ai A￾ = U ￾ I￾{1,...,n} (￾1)|I| |AI |