MMW101Week5.pdf

Universal Sets and Venn Diagrams The universal set is a general set that contains all elements under discussion. John Venn (1843 – 1923) created Venn diagrams to show the visual relationship among sets. Universal set is represented by a rectangle Subsets within the universal...

Universal Sets and Venn Diagrams The universal set is a general set that contains all elements under discussion. John Venn (1843 – 1923) created Venn diagrams to show the visual relationship among sets. Universal set is represented by a rectangle Subsets within the universal set are depicted by circles, or sometimes ovals or other shapes.  Example 1 Determining Sets From a Venn Diagram Use the Venn diagram to determine each of the following sets: a. U U = { O , ∆ , $, M, 5 } b. A A={O,∆} c. The set of elements in U that are not in A. {$, M, 5 } 2 Representing Two Sets in a Venn Diagram Example 2 Determining sets from a Venn Diagram Use the Venn Diagram to determine: a. U b. B c. The set of elements in A but not B d. The set of elements in U that are not in B e. The set of elements in both A and B. The Complement of a Set 9/18/2024 Section 2.3 5 Example 3 Finding a Set’s Complement The Intersection and Union of Sets Example 4 Finding the Intersection of Two Sets Example 5 Finding the Union of Sets Example 6 Performing Set Operations  Example 7 Determining Sets from a Venn Diagram Set to Determine Description of Set Regions in Venn Diagram a. AB set of elements in A or B or Both I,II,III b. (A  B)’ set of elements in U that are not in A  B IV c. AB set of elements in both A and B II d. (A  B)’ set of elements in U that are not in A  B I, III, IV e. A’  B set of elements that are not in A and are in B III f. A  B’ set of elements that are in A or not in B or both I,II, IV Sets and Precise Use of Everyday English Set operations and Venn diagrams provide precise ways of organizing, classifying, and describing the vast array of sets and subsets we encounter every day. Or refers to the union of sets And refers to the intersection of sets  Example 8 Constructing Venn Diagram Some of the results of the campus blood drive survey indicated that 490 students were willing to donate blood, 340 students were willing to help serve a free breakfast to blood donors, and 120 students were willing to do both. a. How many students are willing to only donate blood? b. How many students are willing to only help in serving a free breakfast to blood donors? c. How many students are there in all?