Download Lesson 1 – Types of Sets and Set Notation

F30 – Unit 1 – Set Theory and Logic
Lesson 1 – Types of Sets and Set Notation
Date: _______________
Lesson 1 – Types of Sets and Set Notation
Set – A collection of distinguishable objects
Element – An object in a set
Universal Set – A set of all the elements under consideration for a particular context.
Set Notation:
1) Sets are defined using brackets {}. Each element is placed within the brackets to show they are contained in the set.
Example 1: Fill in the following examples of sets and write the set notation of each.
Fruit
Whole Numbers between 1 and 20
Even Numbers
Set:
Elements:
Common Sets:
The Set of Digits:
The Set of Whole Numbers:
The Set of Real Numbers:
The Set of Natural Numbers:
Set:
Elements:
D = {0,1,2,3,4,5,6,7,8,9}
W = {0,1,2,3,4,5,6…}
R = {… -1, -0.5, 0, 0.5, 1…}
N = {1, 2, 3, 4…}
The Set of Integers:
The Set of Odds:
The Set of Evens:
The Set of Primes:
Set:
Elements:
I = {… -1, 0, 1, 2 …}
O = {1, 3, 5, 7, 9…}
E = {2, 4, 6, 8, 10…}
P = {2, 3, 5, 7, 11, 13…}
Subset – A set whose elements all belong to another set; for example, the set of all odd digits, O = {1, 3, 5…} is a subset
of D, the set of digits.
Complement – All the elements of a universal set that do not belong to a subset of it.
Empty Set – A set with no elements; for example, the set of odd numbers divisible by 2 is the empty set.
Set Notation:
1) If A is a subset of B we write:
2) The complement of A is A’
3) To denote an empty set we write:
A=∈
A = { } or A = ∅
Example 2: Set A = {1, 2, 3, 4, 5,6} and Set B = {2, 4, 6}.
a) If there is a subset denote this using set notation
b) Determine the set B’
c) Determine C, a subset of B, that contains odd integers
F30 – Unit 1 – Set Theory and Logic
Lesson 1 – Types of Sets and Set Notation
Date: _______________
Disjoint – Two or more sets having no elements in common
Finite Set – A set with a countable number of elements
Infinite Set – A set with an infinite number of elements
Example 3: Using set notation give an example of the following:
a) Two disjoint sets
b)A finite set
c) An infinite set
Writing Set Notation for large sets
1) Set up the following:
{x|___ ≤ x ≤ ___}
(you can use any variable)
2) Put your smallest number in the first blank and your largest number in the last blank
3) This is read as: Blank is less than or equal to x which is less than or equal to blank. This means that
whatever you choose for x has to between the two blanks.
Representing Using a Venn Diagram
1) The outside is a representation of the universal set, of all numbers possible
2) A circle is a subset of the universal set
3) If you have a subset of a subset you place the circles on top of each other
U
A
B
A’
U
A∈U
B∈A
A’
- Universal Set
- A is a subset of U
- B is a subset of A
B ∈ A∈ U
- Complement of A
Example 4: Indicate the multiples of 5 and 10, from 1 to 500, using set notation. List any subsets and any
complimentary sets. Represent this as a Venn Diagram.
F30 – Unit 1 – Set Theory and Logic
Lesson 1 – Types of Sets and Set Notation
Date: _______________
Set Notation:
1) The number of elements in a set is denoted as n(A)
2) If A = {1, 2, 3, 4, 5, 6} then n(A) = 6
Example 5: You rescue homeless animals and advertise on a website. You currently have dogs, cats, rabbits,
ferrets, parrots, lovebirds, macaws, iguanas, and snakes.
a) Design a way to organize the animals on the webpage. Use set notation and a Venn Diagram
b) Name and subsets, disjoint sets, and complimentary sets.
c) Create a subset of fur-bearing animals. Write in set notation which set this would be a subset of and also
which set it would be equal to.