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MATH 2311 Section 2.2. Sets and Venn Diagrams A set is a collection of objects. Two sets are equal if they contain the same elements. Set A is a subset.

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Presentation on theme: "MATH 2311 Section 2.2. Sets and Venn Diagrams A set is a collection of objects. Two sets are equal if they contain the same elements. Set A is a subset."— Presentation transcript:

1 MATH 2311 Section 2.2

2 Sets and Venn Diagrams A set is a collection of objects. Two sets are equal if they contain the same elements. Set A is a subset of set B if every element that is in set A is also in set B. The notation for this is A  B. Set A is a proper subset of set B if every element that is in set A is also in set B and there is at least one element in set B that is not in set A. The notation for this is A  B.

3 Sets and Subsets If Set A contains all dogs, and Set B contains all Golden Retrievers, then B  A. However, A  B is not true.

4 An Example of Sets To belong to Set A, you must be over the age of 25. To belong to Set B, you must drive a blue car. Think about which sets you would belong to.

5 Set Union The union of A and B, which is written as c, is the set of all elements that belong either to set A or to set B (or that belong to both A and B). If you answered “yes” to either of the questions, you belong in the set union.

6 Set Intersection The intersection of A and B, which is written as A  B, is the set of all elements that belong to both to set A and set B. If the intersection of two sets is empty (the empty set is denoted by , then the sets are disjoint or mutually exclusive and we write A  B   If you answered, “yes” to both questions, you belong in set intersection.

7 Set Compliment The complement of set A, which is written as A c, is the set of all elements that are in the universal set but are not in set A. If you answered “no” to question A, you belong in the set compliment.

8 Examples: Use the following information to answer the questions: U   1, 2, 3, 4, 5, 6, 7, 8, 9, 10  A   1, 2, 5, 6, 9, 10  B   3, 4, 7, 8  C   2, 3, 8, 9, 10 

9 Venn Diagrams These are also known as “circle diagrams,” and they can be used to represent sets. Shade in A  B A  B A A B B

10 Venn Diagrams Shade in A c (A  B) c A A B B

11 Venn Diagrams Shade in A∩B∩C A∩C A B C A B C

12 Application Draw a Venn Diagram for the following situation: A group of 100 people are asked about their preference for soft drinks. The results are as follows:

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