LN1(PIE)(1) - Principle of Inclusion and Exclusion...

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Unformatted text preview: Principle of Inclusion and Exclusion Principle of Inclusion and Exclusion Let , , …, be arbitrary sets. Then Examples Exercise. Write the formula for using the principle of inclusion and exclusion. Illustration for The red circle means that the elements in the region are counted. Illustration for There are two red circles in the intersection. This means that the elements in the intersection are counted twice. Illustration for We subtracted . Therefore, remove one circle in the intersection. Illustration for Illustration for Illustration for Illustration for Illustration for Illustration for Illustration for Illustration for Exercise. Inside an airplane, we have the following information: a) Twenty passengers speak English b) Forty passengers speak Filipino. c) Thirty passengers speak Chinese. d) Fifteen passengers speak both English and Filipino. e) Twelve passengers speak both English and Chinese. f) Twenty-two passengers speak both Filipino and Chinese. g) Eight passengers speak all the three languages. What is the total number of passengers in the plane? ...
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