Surveys and Cardinal Numbers 2'5

1
Surveys and Cardinal Numbers 2.5
Objective 1 Use Venn Diagrams to visualize a
surveys results.
And means intersection.
Or means union.
Not means complement.
2
Use the Venn diagram to answer the questions
below.
U
A 17
B 11
n ( A )
26
9
n ( B )
20
7
n ( U )
44
n ( A B)
9
n ( A B)
37
3
Objective 2 Use the formula to find n ( A
B) w/o a Venn.
n( A )
n( B )
n(A B)
n( A B)
26
20
9
37
This formula is used to find the Cardinal number
of two sets.
4
Find the missing cardinal number based on the
data below.
n ( A B)
6
n ( A )
17
n ( A B)
?
n ( B )
20
n( A )
n( B )
n(A B)
n( A B)
17
20
6
n( A B)
31
5
Find the missing cardinal number based on the
data below.
n ( A B)
?
n ( A )
490
n ( A B)
710
n ( B )
340
n( A )
n( B )
n(A B)
n( A B)

490
340
710
n(A B)
- n( A B)
-120
n( A B)
120
6
Find the missing cardinal number based on the
data below.
n ( A B)
6
n ( A )
?
n ( A B)
42
n ( B )
18
n( A )
n( B )
n(A B)
n( A B)
?
18
6
42
42 n ( A) 12
30 n ( A)
7
Set A contains 8 letters and 9 numbers, set B
contains 7 letters and 10 numbers. There are 4
letters and 3 numbers common to both sets. Find
the number of element in set A or set B.
n ( A B)
7
n ( A )
17
n ( A B)
?
n ( B )
17
n ( A B) 17 17 7
27
8
Objective 3 Solving Survey problems.
1. Use Surveys description to define sets and
draw Venn diagram.
2. Determine Cardinality of each region.
Start with intersection of the sets, innermost
region, and work outward.
3. Use completed Venn diagram to answer
questions.
9
A pollster asked college students how they
remained informed of world events. Construct a
Venn Diagram for the following responses
only from newspapers,
only from television,
both newspapers and televisions
neither newspapers or televisions.
10
U
NP
TV
b
b
Write a letter b in every region of the diagram
that represents all college students polled that
do not remain informed by TV.
11
U
NP
TV
c
c
c
Write a letter c in every region of the diagram
that represents all college students polled that
remain informed by TV or newspapers.
12
U
NP
TV
7
36
22
10
Put in this specific information 75 college
students in all were surveyed. 29 said they got
their news from newspapers, 43 from TV, and 7
from both newspapers and television.
13
U
NP
TV
7
36
22
10
How many received their news from newspapers or
television?
65
How many did not get news from television?
32
14
Draw a Venn diagram from the following survey
results.
A survey of 120 college students was taken at
registration. Of those surveyed, 75 students
registered for a math course, 65 for an English
course and 40 for both math and English.
15
n (U) 120 n (M) 75 n (E) 65 n (M
E) 40
U
M
E
40
25
35
20
16
U
M
E
40
25
35
20
How many registered for only an English course?
25
How many did not register for either a Math or
English course?
20
17
Homework

• Pg 80
• 3 30,
• Multiples of 3