Let’s develop a proof of the Inclusion-Exclusion formula using high school algebra.
(a) Most high school students will get freaked by the following formula, even though they actually know the rule it expresses. How would you explain it to them?
For any set, S, let MS be the membership function of S:
Let S1; : : : ; Sn be a sequence of finite sets, and abbreviate MSi as Mi . Let the domain of discourse, D, be the union of the Si ’s. That is, we let
and take complements with respect to D, that is,
(f) Finally, explain why (15.18) immediately implies the usual form of the Inclusion- Exclusion Principle:
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