Post on 24-Dec-2015
1. Based on the diagram, what is the total number of students who did participate in volleyball?
15 9 11 6 5 4
12
15 9 11 6 5 4
12
Warm-Up:
Baseball Basketball
Volleyball
VocabularyA set
The elements
Subsets
Empty set/Null set
Universal set
of a set are the objects in a set.
is any well defined collection of “objects.”
consists of elements from the given set.
is the set that contains no elements.
is the set of all possible elements.
*Make sure you leave a few empty line under each word & definition to provide examples and/or illustrations
Ways of Describing Sets
List the elements
Give a verbal description
“A is the set of all integers from 1 to 6, inclusive”
Give a mathematical inclusion rule
A= 1,2,3,4,5,6
A= Integers 1 6x x
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 discussionand 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}
Venn Diagrams
Venn diagrams show relationships between sets and their elements
Universal Set
Sets A & B
1 3
5 8 2 4
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:
U black purple A red white blue green
Types of color
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′?
Combining Sets – Set Union
“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.
A B
Combining Sets – Set Intersection
“A intersect B” is the set of all elements that are in both A and B.
This is similar to the logical “and”
A B
Venn Diagrams
Venn Diagrams use topological areas to stand for sets. I’ve done this one for you.
A B
A B
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
P M
P N
N M
PN
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!