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# ch8 - Chapter 8 Inclusion Exclusion Set notation AB AB AB A...

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Chapter 8: Inclusion Exclusion Set notation: A B A B A B A De Morgan rules: A B = A B A B = A B Counting elements in sets: N the number of elements in the “universe”. N ( A ) the number of elements in the set A . N ( A ) = N - N ( A ). N ( A B ) = N ( A ) + N ( B ) - N ( A B ). N ( A B ) = N ( A B ) = N - N ( A B ) = N - N ( A ) - N ( B ) + N ( A B ).

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N ( F L ) = N - N ( F ) - N ( L ) + N ( F L ). Example 1: There are 100 students. 50 take French, 40 Latin and 20 take both. How many take neither language? Example 2: How many arrangements of the digits 0,1,2,...,9 have their first digit larger than 1 and last digit smaller than 8? Example (SAT question):In a community of 416 people, each person owns a dog or a cat or both. If 316 own dogs, 280 own cats, how many dog owners to not own a cat?
N ( F L ) = N - N ( F ) - N ( L ) + N ( F L ). What about 3 sets? N ( F L G ) = N ( F ) + N ( L ) + N ( G ) - N ( F L ) - N ( F G ) - N ( L G ) + N ( F L G ) N ( F L G ) = N - N ( F L G ) = N - N ( F ) - N ( L ) - N ( G ) + N ( F L ) + N ( F G ) + N ( L G ) - N ( F L G ) Example 3: There are 100 students. 40 take French, 40 Latin, 40 German, 20 take any pair of languages, and 10 take all 3 languages. How many take

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