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Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains elements 1, 3, 5, and 7. *elements do not need to go in any particular order *there are many ways to represent certain sets

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A set with no elements is called an empty set (null or void). Set A, in either case, represents the empty set. Its empty! Noooo!

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A universal set is the set of ALL elements. Set A represents the universal set. I want everything!

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The union of sets (A U B) is the set of all elements in A or B. The union of two students math skills!

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The intersection of sets (A B) is the set of all elements in A and B. Our intersection will be that sandwich if you SHARE it!

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When working with sets, Venn Diagrams become very useful in determining the truth of statements. A BC Do you swear to tell the truth, the whole truth, and nothing but the truth?

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The shaded region represents all of set A. C A B

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The shaded region represents all of set B. C A B

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The shaded region represents all of set C. C A B

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The shaded region represents C A B

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C A B

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C A B

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C A B

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Notice and C A B are the same! C A B

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When working with sets, Venn Diagrams become very useful in determining the truth of statements. The Venn Diagrams on the previous slide showed the statement was true.

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Venn Diagrams also serve as a nice way to represent data.. At a restaurant, Bella, Edward, Jacob, Alice, and Jasper were asked if they had ordered (not eaten ) any of the following: chicken marsala, lasagna, or coke. 3 people ordered chicken marsala (Edward, Alice, Jacob). 2 people ordered lasagna (Bella and Jacob). 3 people ordered coke (Alice, Bella, and Jasper). 1 person ordered both chicken marsala and lasagna (Jacob).

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Jasper (coke) chicken marsala lasagnacoke Jasper Alice Edward Bella Jacob Edward (chicken marsala) Alice (chicken marsala, coke) Bella (lasagna, coke) Jacob (chicken marsala, lasagna)

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Click on the following link to view a brief video clip. Resume the PowerPoint after. Venn Diagram and Instruments

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Now go to the following website and practice working with Venn Diagrams! Time for Fun!

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SETS 2 – Union and Intersection. UNION of sets – to perform the union of two sets, we just list the elements of both sets. It is not necessary to repeat.

SETS 2 – Union and Intersection. UNION of sets – to perform the union of two sets, we just list the elements of both sets. It is not necessary to repeat.

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