Sets and Set Operations

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Sets and Set Operations by Mind Map: Sets and Set Operations

1. Venn Diagrams

1.1. Once you review how to shade venn diagrams based on the sets that are listed, please continue to practice on this link. Be sure to save it as a pdf and submit it to the google classroom assignment.

2. Definitions

2.1. Set: a set is a collection of objects or things

2.2. Elements: the objects or things in a set

2.3. Well-Defined: sets are called well-defined if there is a way of determining for sure whether a particular item is an element of the set

2.4. Roster Notation ( Listing Notation): a method of describing a set by listing each element of a set inside { and }, which are called set braces. PS no repeat elements

2.5. Cardinal Number: the number of elements in the set denoted n(A), where A is a set.

2.6. Equal: Two sets are considered equal if they contain exactly the same elements

2.7. Set-Builder Notation: A more concise way of way of describing a set. lists the rules that determine whether an object is an element of the set

2.8. Empty Set: a set that has no element

2.9. Universal set: the set of all possible elements of any set used in the problem

2.10. Subset: Let A, B be sets. A is a subset of B if every element of A is in B

2.11. Venn Diagram: consists of a rectangle, representing the universal set and various closed figures within the rectangle each representing a set.

2.12. Improper subset: Let A, B be sets where A= B. Since A contains every element of B, then A is an improper subset of B.

2.13. Intersection

2.14. Mutually Exclusive

2.15. Union

2.16. Complement: The set of all elements in the universal set that are not in the specified set

3. Practice Vocabulary

3.1. more Vocabulary Practice

4. Identifying well-defined sets

4.1. the set of all movies directed by Alfred Hitchcock

4.1.1. This set is well-defined; either a movie was directed by Hitchcock, or it was not.

4.2. the set of all great rock-and-roll bands

4.2.1. This set is not well-defined; membership is a matter of opinion. Some people would say that the Ramones (one of the pioneer punk bands of the late 1970s) are a member, while others might say they are not. (Note: The Ramones were inducted into the Rock and Roll Hall of Fame in 2002.)

4.3. the set of all possible two-person committees selected from a group of five people

4.3.1. This set is well-defined; either the two people are from the group of five, or they are not.

5. Standards

5.1. A2.S.CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). There are no assessment limits for this standard. The entire standard is assessed in this course.

5.2. A2.S.CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. There are no assessment limits for this standard. The entire standard is assessed in this course.

5.3. A2.S.CP.A.3 Know and understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B

6. Universal Set and Subset

6.1. Universal Set is usually denoted by U

6.1.1. ○ Example of a Universal Subset

6.1.2. § U = {all the letters of the alphabet (uppercase and lowercase} ○ Example of a subset of U {a,I, z}

6.2. ○ Determining Subsets:

6.2.1. Let B ={States| States in the United States that start with a letter A} A. A = {Alabama, Athens} NOT A SUBSET B. A = {Alabama, Arkansas, Alaska} Yes, SUBSET C. A = {} Yes, SUBSET

7. Intersection

7.1. hat is an Intersection? (Set Theory)

7.2. Let A = {1 2 3 4 5 6} and Let B = { 1 3 5 7 9}

7.2.1. A ∩ B = {1, 3, 5}

7.3. Once you get to this part, please visit this site for practice and more examples

8. Mutually Exclusive Sets:

8.1. - Let A = {0 2 4 6 8}

8.2. - Let B = {1 3 5 7 9}

8.3. - Remember: Two sets A and B are mutually exclusive (or disjoint) if they have no elements in common, that is, if A ∩ B = ∅.

8.4. - Are A and B mutually exclusive?

9. Union of sets

9.1. Union of Sets

9.2. Let A = {1 2 3 4 5 6}

9.3. Let B = { 1 3 5 7 9}

9.4. § A ∪ B =

9.5. Venn Diagram

10. Complement of a set

10.1. The complement of set A, denoted by A', is A'={x|x in U and x not in A}.

10.2. Example:

10.2.1. Let U = {A,B,C,D,E}, and A = {A,B} A' = {C,D,E}

10.2.2. Let U = the set of integers and A = {all the even integers} A' = {all the odd integers}