13 11 students use both windows and mac os w m 11

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Unformatted text preview: tudents use at least one of the operating systems ⇒ #(W ∪ M ∪ L) = 46 11 students use both Windows and Linux ⇒ #(W ∩ L) = 11 2.13 11 students use both Windows and Mac OS ⇒ #(W ∩ M ) = 11 Example 10: Venn diagram Venn Diagrams; Probability Laws Use the above information to complete a three-way Venn diagram. Set Operations and Relations Venn Diagram 2.14 Notes Example 10 (cont’d) Venn Diagrams; Probability Laws Notes Using the Venn diagram summarizing the distribution of operating system use previously described, Let W denotes Windows, M denotes Mac OS, and L denotes Red Hat Linux Enterprise. Calculate the following: 1 #(W c ∩ M c ) Set Operations and Relations 2 P( W c ∪ M c ) Venn Diagram 3 #(W ∪ M ∪ L) Solution. 2.15 More Laws Venn Diagrams; Probability Laws Let A, B , and C be subsets of Ω Distributive law A ∩ (B ∪ C ) = (A ∩ B ) ∪ (A ∩ C ) A ∪ (B ∩ C ) = (A ∪ B ) ∩ (A ∪ C ) Associative law Set Operations and Relations Venn Diagram A∪B =B∪A A∩B =B∩A Commutative law A ∩ (B ∩ C ) = (A ∩ B ) ∩ C A ∪ (B ∪ C ) = (A ∪ B ) ∪ C 2.16 Notes Summary Venn Diagrams; Probability Laws Notes In this lecture, we learned Set operations: union, intersection Set relations: mutually exclusive, Exhaustive, Partition Venn diagram: a handy tool to visualize set relationships Set Operations and Relations Venn Diagram Probability laws: general addition rule, complement rule 2.17 Notes...
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