Use mathematical induction to prove the general inclusion/exclusion rule: If A1, A2,...
Chapter 9, Problem 48(choose chapter or problem)
Use mathematical induction to prove the general inclusion/ exclusion rule:
If \(A_{1}, A_{2}, . . . , A_{n}\) are finite sets, then
N(\(A_{1} ∪ A_{2} ∪ · · · ∪ A_{n}\))
(The notation \(\sum_{1 \leq i<j \leq n} N\left(A_{i} \cap A_{j}\right.\) ) means that quantities of the form N(Ai ∩ Aj ) are to be added together for all integers i and j with 1 ≤ i < j ≤ n.)
Text Transcription:
A_1, A_2, . . . , A_n
A_1 ∪ A_2 ∪ · · · ∪ A_n
sum_1 leq i<j leq n N (A_i cap A_j
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