13.2 Counting the Elements of Sets Solution Key
List the integers from 1 to 10 inclusive that are
1. odd. {1,
3, 5, 7, 9}
2. multiples of 2. {2,
4, 6, 8, 10}
3. odd and multiples of 2. {}
(There are none!)
4. odd or multiples of 2. {1,
2, 3, 4, 5, 6, 7, 8, 9, 10}
List the integers from 1 to 20 inclusive that are
5. multiples of 4. {4,
8, 12, 16, 20}
6. multiples of 3. {3,
6, 9, 12, 15, 18}
7. multiples of 4 and multiples of 3. {12}
(12 is the only number in both
sets.)
8. multiples of 4 or multiples of 3.
{3, 4, 6, 8, 9, 12, 15, 16, 18, 20}
Notice that, as we talk about these as sets, the and
values are the ones in both/all of the sets, and the or
values are the ones in any of the sets.
Advanced Math Topics
p. 1
Tuesday, December 4, 2007
9. Draw a Venn diagram that shows the multiples of 3 and the multiples of 5 from 1 to 30
inclusive.
Multiples of 5
Multiples of 3
5
15
3
20
9
18
10
6
12
30
21
25
24
27
10. Which numbers are multiples of 3 and of 5?
{15, 30}
The numbers in the
overlapping circles are the numbers which are in
both sets.
11. How is this shown in the Venn diagram?
Advanced Math Topics
p. 2
Tuesday, December 4, 2007
A marketing representative gave supermarket customers a sample taste of a new soft drink. The
results are shown in the table.
12. How many customers are men?
30 customers are
men.
13. How many customers disliked the new soft drink?
24 customers disliked
the new soft drink.
14. How many customers are men
and disliked the new soft
drink?
14 customers are
men and disliked
the new soft drink.
15. How many customers are men or disliked the new soft drink? 30
+ 24 – 14 = 40
customers are men or disliked the new soft drink.
Advanced Math Topics
p. 3
Tuesday, December 4, 2007