150 men live in a certain town:
85 are married
70 have a cell phone
75 own a car
55 are married and have a cell phone
35 have a cellphone and a car
40 are married and have car
30 are married, have a car and have a cellphone. How many men are single and do not have a car? How many men are single and do not have either a car or a cellphone?
a - 150-85=65 single
b - 150-70= 80 w/o cellphone
c - 150-75= 75 who own a car
d - 150-55= 95 single w/o cellphone
e - 150-35= 115 w/o cell phone and car
f - 150-40= 110 single without a car
g - 150-30= 120 single. w/o car and cellphone
You could use Venn diagrams or use the formula:
N(car OR cell OR married)
= N(car) + N(cell)) + N(married) - N(car AND cell) - N(car AND married) - N(cell AND married) + N(car AND car AND married)
=75+70+85-35 - 40 - 55 + 30
= 130
but there were 150 men considered, so 20 have no phone or car and are single
My Venn diagrams gave me the same answer, but it also shows many other subsets,
e.g. the number of married men who have a car but no cellphone is 10, etc
To answer this question, we need to use the principles of set theory and Venn diagrams. Let's break down the information given.
Let's define the following events:
M = Men in the town
S = Single men
C = Men who have a cell phone
R = Men who have a car
According to the given information:
Total number of men (M) = 150
Number of married men (M ⋂ S') = 85
Number of men with a cell phone (C) = 70
Number of men with a car (R) = 75
Number of men who are married and have a cell phone (M ⋂ C) = 55
Number of men who have a cell phone and a car (C ⋂ R) = 35
Number of men who are married and have a car (M ⋂ R) = 40
Number of men who are married, have a car, and have a cell phone (M ⋂ R ⋂ C) = 30
To find the number of single men who do not have a car, we need to subtract the number of men who are married from the total number of men:
S = M ⋂ S'
Single men who do not have a car = S - (M ⋂ R)
Single men who do not have a car = 150 - 85 - 40
Single men who do not have a car = 25
To find the number of single men who do not have either a car or a cell phone, we need to subtract the number of men who have a cell phone or a car from the total number of single men:
Single men who do not have either a car or a cell phone = S - (C ⋃ R)
Single men who do not have either a car or a cell phone = 150 - (70 + 75 - 35)
Single men who do not have either a car or a cell phone = 150 - 105
Single men who do not have either a car or a cell phone = 45
Therefore, there are 25 men who are single and do not have a car, and there are 45 men who are single and do not have either a car or a cell phone.