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Warm-Up: 1. Based on the diagram, what is the total number of students who did participate in volleyball? 15 9 11 6 5 4 12 Volleyball Set Theory *Make sure you leave a few empty line under each word & definition to provide examples and/or illustrations Vocabulary A set is any well defined collection of “objects.” The elements of a set are the objects in a set. Subsets consists of elements from the given set. Empty set/Null set is the set that contains no elements. Universal set is the set of all possible elements. Ways of Describing Sets List the elements A= 1,2,3,4,5,6 Give a verbal description “A is the set of all integers from 1 to 6, inclusive” Give a mathematical inclusion rule A= Integers x 1 x 6 Some Special Sets The Null Set or Empty Set. This is a set with no elements, often symbolized by or {} The Universal Set. This is the set of all elements currently under consideration, and is often symbolized by U Universal Sets The universal set is the set of all things pertinent to a given discussion and is designated by the symbol U Example: U = {all students at Brandeis} Some Subsets: A = {all Computer Technology students} B = {freshmen students} C = {sophomore students} What?!? Find the Subsets What are all the subsets of {3, 4, 5} {} or Ø {3}, {4}, {5} {3,4}, {3,5}, {4,5} {3,4,5} Try it with a partner Page 197 (20, 21) Venn Diagrams Venn diagrams show relationships between sets and their elements Sets A & B Universal Set 5 8 2 4 1 3 Venn Diagram Example Set Definition U= {1, 2, 3, 4, 5, 6, 7, 8} Set Complement ~A or A′ “A complement,” or “not A” is the set of all elements not in A. *What the others have that you don’t* Practice: Types of color U black purple A red white blue green Universal set U = What is the complement of set A? More Practice: U = {1, 2, 3, 4, 5} is the universal set and A = {2, 3}. What is A′? U = {a, b} is the universal set and T = {a}. What is T′? U = {+, -, x, ÷, =} is the universal set and A = {÷, =}. What is A′? Try it with a friend Page 197 (26, 27) Page 198 (39) Venn Diagrams Here is another one A B What is the A′? A moment to Breath The moment is over Combining Sets – Set Union A B “A union B” is the set of all elements that are in A, or B, or both. This is similar to the logical “or” operator. Combining Sets – Set Intersection A B “A intersect B” is the set of all elements that are in both A and B. This is similar to the logical “and” Venn Diagrams Venn Diagrams use topological areas to stand for sets. I’ve done this one for you. A B AB Venn Diagrams Try this one! A B AB Examples A {1,2,3} B {3,4,5,6} • A B {3} • A B {1,2,3,4,5,6} Try it on your own! Let P = {b, d, f, g, h}, M = {a, b, c, d, e, f, g, h, i, j}, N = {c, k} P M PM PN NM PN Try it on your own! Page 218 (10, 12, 14, 16, 18, 20) Product?!? Given set D and F, find D x F D = {1, 3, 5}, F = {0, 2} Given set R and S, find R x S R = {Bob, Rose, Carlos}, S = {Sheila} Pair in-class-mini-project Please pick a student with whom you KNOW you CAN work and be PRODUCTIVE Assignment: Develop/Create a book explaining all four Vocabulary words from the SET THEORY topic (Complement, Union, Intersection, Product). Use a self-created example for each concept. Your audience - a group of elementary students who learn better when the teacher utilizes images/drawings. Be creative!!! Make sure your work makes sense, you might have to present it! Wrap-Up: Summary Home-Learning Assignment #2: Page 198 (46) Page 199 (53) Page 219 (22) Page 220 (40, 46)

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posted: | 10/4/2012 |

language: | English |

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