PIE (Principle of Inclusion-Exclusion) a-A-,之4n+ 三1 1<i<n 1≤i<j≤n …+(-1)n-1|A1∩.∩An ≥-11门4 IC{1,,n} I≠0PIE (Principle of Inclusion-Exclusion) ￾ ￾ ￾ ￾ ￾ ⇥ n i=1 Ai ￾ ￾ ￾ ￾ ￾ = ￾ 1￾i￾n |Ai| ￾ ￾ 1￾i<j￾n |Ai ⇥ Aj |+ ··· + (￾1)n￾1|A1 ⇤ ··· ⇤ An| = ￾ I￾{1,...,n} I￾=￾ (￾1)|I|￾1 ￾ ￾ ￾ ￾ ￾ ￾ i￾I Ai ￾ ￾ ￾ ￾ ￾