MATH 2311 Section 2.2.

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Presentation transcript:

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 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 .

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. When using subset notation, you cannot reverse the order (except if the sets are equal)

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.

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.

Set Intersection Must be in the overlap of sets A and B 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.

Set Compliment The complement of set A, which is written as Ac, 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.

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

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

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

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

Application Popper 01: Question numbers are in the diagram a. 5. b. 10 Application Popper 01: Question numbers are in the diagram a. 5 b. 10 c. 15 d. 20 e. 25 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: Q1: A Q2: C Q3: D Q4: D Q5: D Diet Coke Coke Qust 1 Qust 4 Qust 3 Qust 2 Pepsi Qust 5