Venn Diagrams and Set Operations

1. In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 24 said they were going to buy a new washer. Of these, 6 were going to buy both a car and a refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy a washer and a refrigerator. One person indicated that she was going to buy all three items.
Construct a Venn diagram, label your diagram clearly. Use your diagram to answer the following questions:
(a) How many were going to buy only a car?
(b) How many were going to buy only a washer?
(c) How many were going to buy only a refrigerator
(d) How many were going to buy a car and a washer but not a refrigerator?
(e) How many were going to buy none of these items?

2. A survey of a group of people produced the following results: there were 25 people with brown eyes and 15 people with blonde hair. If 10 people had both brown eyes and blonde hair and 23 people had neither, how many people were interviewed?

3.) A survey of residents in a small town showed the following:
29 ate beef,
13 ate both beef and fish,
6 ate all types
26 ate fish
11 ate both fish and poultry
7 ate none of them
25 ate poultry
18 ate both beef and poultry

Draw a Venn diagram. Label your diagram clearly. Use your diagram to answer the following questions:
(a) How many ate fish, but not poultry or beef?
(b) How many ate poultry and fish, but not beef?
(c) How many ate only beef?
(d) How many ate nothing or only poultry?

keywords: union, intersection, complement

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