Download Algebra 107 Unit 4 Sets

Integrated Algebra Unit 4 Sets
Sets & Set Builder Notation
Name:___________________________________________________
Date:_____________
Period:_____
Do-Now
1) Solve the following equations.
a) 3x – 10 = 11
b) x + 7x – 9 = 7
2) Determine whether the following sets are closed under the given operation.
a) Positive integers;
b) Odd integers;
addition
multiplication
c) {0, 1, 2};
multiplication
Sets & Set-Builder Notation
Vocabulary: A ____________ is a collection of unique elements. Elements in a set do not _______________.
Methods of describing sets:
1)
2)
3)
Method #1: Roster Form
THERE IS NO ROSTER
Definition:
METHOD (YOU CAN’T
LIST THEM OUT) FOR
Example: {2, 3, 4, 5, 6} is the set of integers from 2 to 6.
________________,
__________________ &
Example: {1, 2, 3, 4, …} is the set of _____________________.
_________________.
Practice Examples:
Put each of the following in roster form.
1) The set of integers from 1 to 4.
2) Whole numbers between 5 and 9.
3) Even natural numbers less than 11.
4) Integers greater than 8.
Method #2: Set Builder Notation
Review of Symbols:
R=
New Symbols:
=
Z=
N=
W=
=
Q=
or you can use the colon :
~Q =
Example:
Given the set: 3, 4, 5, 6, 7
In roster form:
In Set Builder Notation:
Practice Examples:
Write each of the following in set builder notation.
1) The set of integers from 1 to 4.
2) Whole numbers between 5 and 9.
3) Even natural numbers less than 11.
4) Integers greater than 8.
Method #3: Interval Notation
Interval notation is an alternative to expressing your answer as an ___________________.
Symbols:
(
Example:
As an inequality: ___________________
[
In interval notation: __________________
Practice Examples:
Write each of the following in interval notation.
1) 4 ≤ x < 9
2) –3 ≤ x ≤ 2
3) Even natural numbers less than 11.
4) Integers greater than 8.
Mixed Practice:
1) Given the set of 5, 6, 7, 8, write it in roster form and in set builder notation.
2) Given the interval [8, 10], what is the inequality?
3) Given: {-3, -2, -1, 0, 1, 2, 3} write it in set builder notation.
Subsets
Definition: Set A is a subset of Set B if and only if ______________________________________________.
Notation:
Proper Subset: A subset is proper if __________________________________________________________.
Examples:
1) {5, 10, 15, 20} is a subset of {0, 5, 10, 15, 20, 25, 30} because
__________________________________________________________________________.
2) Is {2, 4, 6, 8, 10, 12} a subset of the set of positive even integers?
3) Is W(Whole #’s) a subset of N (Natural #’s)?
4) Is {1, 2, 3, 4} a proper subset of {1, 2, 3, 4, 5, 6}?
5) Is {-4, -2, 0, 2, 4} a proper subset of {4, 2, 0, -2, -4}?
Complement of a Set
Definition:
Notation:
Example: If U = {1, 2, 3, 4, 5} and A = {2, 4}, then A` = _____________.
Practice Examples:
Given U = {0, 3, 5, 7, 11, 17}
X = {3, 5, 7}
J = {5, 7, 11, 17}
1) Find: X` =
J` =
2) Is X a subset of U? If so, is it proper?
3) Is X a subset of J? If so, is it proper?
Mixed Practice Examples:
Express each in roster form, set builder notation, and interval notation.
1) Odd positive integers
2) Whole number between 1 and 11
Determine whether each statement is true or false:
3) The set of all counting numbers is a subset of the set of all natural numbers.
4)
{6, 0,11} is a subset of Z
5)
{January, February, March, April} is a subset of the months in a year
For each of the following, determine if the first set is a proper or an improper subset of the second set:
6) {1, 4,5},{5,1, 4}
7)
{2,4,6,8,10}, {2,4,6,8,10,12,14,16,…}
8)
{H, A, T}, {M, A, T, H}