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Section 1.3 Intersection and Union of Sets solutions.notebook
1
September 21, 2016
Sep 157:01 PM
Section 1.3: Intersection and Union of Two Sets
Section 1.3 Intersection and Union of Sets solutions.notebook
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September 21, 2016
Sep 1110:18 PM
Exploring the Different Regions of a Venn Diagram
There are 6 different set notations that you must become familiar with.
Consider the following set: U = {the set of all integers from -3 to +3}U = {A = {the set of non-negative integers}A = {B = {the set of integers divisible by 2}B = {
Section 1.3 Intersection and Union of Sets solutions.notebook
3
September 21, 2016
Sep 129:43 PM
Set Notation Meaning Venn Diagram Answer
A∪B
(A union B)
any element that is in either of the sets
(A or B)The element has to be in at least one of the sets and may be in both
{2,0,1,2,3}
A∩B
(A intersect B)
Only elements that are in both A and B
(A and B)Elements common to both located in the overlap
{0,2}
A\B
set A minus set B
Elements found in set A but excluding the ones that are also in set B
{1,3}
U: {3, 2, 1, 0, 1, 2, 3}
A: {0, 1,2,3}
B: {2,0,2}
Section 1.3 Intersection and Union of Sets solutions.notebook
4
September 21, 2016
Sep 75:37 PM
Set Notation Meaning Venn Diagram Answer
A'
(A complement or not A)
all elements in the universal set outside of A
{2,1,3}
(A∪B)'
not(A union B)
not (A or B)
elements that are outside A and B
{1,3}
(A∩B)'
not(A and B)
not (A intersect B)
elements outside the overlap of A and B
{1,3,2,1,3}
U: {3, 2, 1, 0, 1, 2, 3}
A: {0, 1,2,3}
B: {2,0,2}
Section 1.3 Intersection and Union of Sets solutions.notebook
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September 21, 2016
Sep 1110:55 PM
A BA B
Disjoint SetsSets with Common Elements
n(A∪B) = n(A) + n(B)n(A∪B) = n(A) + n(B) - n(A∩B)
This is called the Principle of Inclusion and Exclusion. We subtract the elements in the intersection so they are not counted twice.
Clarification of A ∪ B(or)
Section 1.3 Intersection and Union of Sets solutions.notebook
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September 21, 2016
Sep 75:37 PM
Clarification of A ∩ B
Disjoint sets: no common elements
n(A∪B) = n(A) + n(B) n(A∩B) or
(and)
Section 1.3 Intersection and Union of Sets solutions.notebook
7
September 21, 2016
Sep 153:06 PM
1. The diagrams below represent a class of children. G is the set of girls and F is the set of children who like fencing. Decide which diagram has the shading which represents:
(a) girls who like fencing
(b) girls who dislike fencing
(c) boys who like fencing
(d) boys who dislike fencing
Section 1.3 Intersection and Union of Sets solutions.notebook
8
September 21, 2016
Sep 153:14 PM
2. Jamaal surveyed 34 people at his gym. He learned that 16 people do weight training three times a week, 21 people do cardio training three times a week, and 6 people train fewer than 3 times a week.
A) How many people do cardio and weight training 3 times a week? Use a Venn diagram and the Principle of Inclusion and Exclusion to answer the question.
B) How many people do only weight training?
C) How many people do only cardio training?
Section 1.3 Intersection and Union of Sets solutions.notebook
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September 21, 2016
Sep 154:22 PM
3. Morgan surveyed the 30 students in her mathematics class about their eating habits.
– 18 students eat breakfast
– 5 of the 18 students also eat a healthy lunch
– 3 students do not eat breakfast and do not eat a healthy lunch.
How many students eat a healthy lunch? Use a Venn diagram and the Principle of Inclusion and Exclusion to answer the question.
Section 1.3 Intersection and Union of Sets solutions.notebook
10
September 21, 2016
Sep 154:44 PM
4. Tyler asked 55 people if they like Criminal Minds or Chicago Fire.
8 people didn't like either show
20 people liked Criminal Minds
38 people liked Chicago Fire
Determine how many people liked both shows, how many only liked Criminal Minds, and how many people liked only Chicago Fire. Use a Venn diagram and the Principle of Inclusion and Exclusion.
Section 1.3 Intersection and Union of Sets solutions.notebook
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September 21, 2016
Sep 154:57 PM
5. Jason asked 100 people if they liked Pepsi or 7UP.
12 people didn't like either drink
18 liked both Pepsi and 7UP
25 people liked only 7UP
Determine how many people liked only Pepsi.
Section 1.3 Intersection and Union of Sets solutions.notebook
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September 21, 2016
Sep 156:52 PM