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 threeway 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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 Spring '08
 MARTIN
 Probability

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