PIE (Principle of Inclusion-Exclusion) A1,A2,...,An U universe AinA2n…An=(-1)川|Al IC{1,.,n} Ar=∩A, Ao=U i∈1PIE (Principle of Inclusion-Exclusion) A1, A2,...,An ￾ U universe ￾ ￾A1 ⇥ A2 ⇥ ··· An ￾ ￾ = AI = ￾ i￾I Ai A￾ = U ￾ I￾{1,...,n} (￾1)|I| |AI |