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3.1 Types of Sets and Set Notation (Solutions).notebook
1
February 10, 2015
Oct 99:12 AM
Chapter 3:
Set Theory and Logic
1.1 Page 2
3.1 ‐
Types of Sets and Set Notation
3.1 Types of Sets and Set Notation (Solutions).notebook
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February 10, 2015
Oct 99:13 AM
SET
ELEMENT
A collection of distinguisable objects
ex. Whole Numbers W = {0, 1, 2, 3, ...}
A particular object in a set
ex. 2 is an element of the whole number set
UNIVERSAL SETA set of all elements considered for any context
ex. Digits D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
EMPTY SETA set with no objects Empty Set Notation { } or 0
ex. Grade 11 students in Math 621A
SUBSETA set whose elements belong to another set
ex. The set of prime numbers P = {2, 3, 5, 7}is a subset of the set D = Digits Notation: P D
COMPLEMENTAll elements of a universal set that do not belong to a subset of it
ex. P' = {0, 1, 4, 6, 8, 9} is the complement to P
DISJOINTTwo or more sets that have no common elements
ex. The set of Islanders from here, and the set of Islanders from away
INFINITE SET
FINITE SETA set with a countable number of elements
ex. The number of people in this class
A set with an infinite number of elementsex. The set of natural numbers N = {1, 2, 3, ...}
Oct 151:07 PM
Remember Number Sets
Natural (N) {1, 2, 3, 4, .... }
Whole (W) {0,1, 2, 3, 4, .... }
Integers(I){...,4,3,2,1,0,1, 2, 3, 4, ....}
Even (E) {2, 4, 6, 8, ...}
Odd (O) {1, 3, 5, 7, 9, ...}
Rational (Q) (Can be written as a fraction decimals terminate or repeat) {...3/2, ... ,0,....., 2,...,9 1/4,....}
Irrational (Cannot be written as a fraction,decimals do not terminate or repeat.){.....∛7,.,e,..π,..... }
Reals (R) (The combination of Rational and Irrational numbers.)
3.1 Types of Sets and Set Notation (Solutions).notebook
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February 10, 2015
Oct 99:42 AM
Venn Diagrams
Oct 151:17 PM
Let U={integers from 10 to 10}
E={Multiples of 2}
S={Multiples of 3}
Draw a Venn diagram.
Example 1
3.1 Types of Sets and Set Notation (Solutions).notebook
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February 10, 2015
Oct 151:15 PM
Given the universal set
U={A,B,C,D,E,F,G,1,2,3,4,5,6,7,8,9,0}
S={characters formed with straight lines only}
C={characters formed with curves only}
Draw a Venn daigram.
Example 2
Mar 610:06 AM
• Joanne recorded the possible numbers that can occur in an outcome table when a sixsided die is rolled.
a. Display the following sets in one Venn diagram.Ø rolls that produce an odd numberØ rolls that produce a multiple of 3
b. In how many ways can a roll occur that is not an odd nor a multiple of 3?
Example 3
3.1 Types of Sets and Set Notation (Solutions).notebook
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February 10, 2015
Mar 78:30 AM
Page 155 # 2
Example 4
Mar 78:31 AM
• A square number, such as 1, 4, 9, or 16, can be represented as a square array.a. Determine a pattern you can use to determine any square number.b. Determine how many natural numbers from 1 to 200 are:
Ø even and squareØ odd and squareØ not square
c. How many numbers are square?
Example 5
3.1 Types of Sets and Set Notation (Solutions).notebook
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February 10, 2015
Oct 910:31 AM
p. 154
# 1, 3 6, 8
Oct 910:18 AM
Of a group of 50 students:30 enjoy playing volleyball25 enjoy playing basketball7 do not enjoy either sport
Draw a Venn diagram to illustrate this situation.
Example 5
3.1 Types of Sets and Set Notation (Solutions).notebook
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February 10, 2015
Oct 910:18 AM
There are 100 people in a school:20 do not like sports8 enjoy only hockey,12 enjoy only hockey and volleyball,10 enjoy all three15 enjoy hockey and cricket2 only enjoy cricket7 enjoy volleyball and cricket only
Draw a Venn diagram for this situation.
How many students enjoy:
a) hockey
b) volleyball
c) cricket or volleyball
U: { all students }H: { hockey }V: { volleyball}C: { cricket }
H V
C
Example 6
Oct 910:20 AM
p. 157
# 11 13, 17
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