Name:



Name: ______________________________ Date: ___________ Period: ______ Algebra IC I: Set TheoryWhat you’ll learn: Perform set operation: union, intersection, complement, and cross product. Use Venn diagram, union and intersection.Did you remember?Natural Numbers:Whole Numbers:Integers:Rational Numbers:Irrational Numbers:Real Numbers:A set is_______________________________________________________________________ ________________________________________________________________________. C= {a, e, i, o, u} BracesCapital Letters such as A, B, C... Note: There is two ways to write a set:Set-Builder notation: Roster Form:Example: 1: The set of all numbers x such that x is a natural number. Roster form N= {1, 2, 3, 4, 5,…} Set-builder notation N= {x|x is a natural number} and it reads the set of all numbers x such that x is a natural number.Your turn: Write the set in roster form and in set-builder notation: M is the set of integers that are greater than 4Answer: Roster form: Set-builder notation:Note: ABA subset is a set whose elements are also contained in another set. The symbol means “is a subset of” “. AB and the empty set is a subset of any set. ?A Empty Set: There are no elements in the set. The empty set is a subset of any set.Example 1: Given the sets Let A={1,2,3,4,5….} and B={1,3,5,7…}.Is B a subset of A? Answer: _____________________________3.8 Intersection:Intersection: Example: Given the sets A= {1, 2, 3, 4, 5} and B= {2, 4, 6, 8}.Find AB. Draw a Venn Diagram. Answer: Your turn: Given the sets. . Find .Draw a Venn Diagram.Union: Example: Given the sets. .Draw a Venn Diagram.Answer:Your Turn: Given the sets Universal Set: It is a set which contains all elements being considered in the given problem. Notation U.Example: U= {a, b, c, d, e, f} A= {a, c, b} B= {e, b, a}. Complete the Venn Diagram BAUAB=AB= Note: Complement of a set A is the set of all elements in the given universal set U that are not in set A. Notation A’Example: Given the set U= {a, b, c, d, e, f} , A= {a, c, b} and B= {e, b, a}Find A’ A’= Your turn B’=Now is your turn11Volleyball 10 11Problem 1: At Vanessa’s high school, 32 girls play volleyball and 35 girls play basketball. Of these, 11 play both volleyball and basketball.Which of these diagrams best represents these numbers? Basketball 3 24 BasketballVolleyball 21 A C Basketball 13Volleyball 32 11 Basketball 24Volleyball 21 11 Basketball11 35B D E 4 6 M7 Problem 2: The Venn diagram below shows the number of students, out of a class of 30, who earned an A in mathematics (M) 13and an A in English (E). How many students: 1. Earned an A in mathematics?2. Earned an A in English? 3. Earned an A in both mathematics and English? 4. Did NOT earn an A in math and did NOT earn an A in English? 5. Earned an A in math but NOT English? 6. Earned an A in English but NOT in math? 9 Cheese 12 Bacon 11Problem 3: This Venn Diagram shows salad topping used for 100 salads in a cafeteria. B=bacon, CH=cheese, CR=croutonsHow many salads had:7 10 8 25 Croutons CCCroROUTONS 1. Just bacon as a topping? 2. Just bacon and cheese? 3. Just croutons and bacon? 4. All three topping? 5. No topping? The Cartesian product (Cross Product) AXB (read “A cross B”) of two sets A and B is defined as the set of all order pairs (a, b) where “a” is a member of A and “b” member of B. Example If A = {1, 2, 3} and B = {a, b} find AXB So AXB = ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download