Sets (Chapter 2) 71EXERCISE 2F
1 A survey was conducted with a group of teenagers to see how
many liked going to the cinema (C) and ice-skating (I). The
results are shown in the Venn diagram. Determine the number
of teenagers:
a in the group
b who like going to the cinema
c who like at least one of these activities
d who only like ice-skating
e who do not like going ice-skating.2 The Venn diagram alongside describes the member
participation of an outdoor adventure club in rock-climbing
(R) and orienteering (O). Determine the number of members:
a in the club
b who go rock-climbing
c who do not go orienteering
d who rock-climb but do not orienteer
e who do exactly one of these activities.3 A team of 24 swimmers took part in a competition. 15 competed in freestyle, 11 competed in backstroke,
and 6 competed in both of these strokes. Display this information on a Venn diagram, and hence
determine the number of swimmers who competed in:
abat least one of these strokes
c freestyle but not backstroke d neither stroke
e exactly one of these strokes.
4 In a building with 58 apartments, 45 households have children, 19 have pets, and 5 have neither
children nor pets. Draw a Venn diagram to display this information, and hence determine the number
of households which:
a do not have children b have children or pets or both
c have children or pets but not both d have pets but not children
e have children but not pets.
5 In a class of 36 girls, 18 play volleyball, 13 play badminton, and 11 play neither sport. Determine the
number of girls who play both volleyball and badminton.
6 At their beachhouse, Anna and Ben have 37 books. Anna has read 21 of them and Ben has read 26 of
them. 2 of the books have not been read at all. Find the number of books which have been read by:
a both Anna and Ben b Ben but not Anna.
7 On a particular day, 500 people visited a carnival. 300 people rode the ferris wheel and 350 people
rode the roller coaster. Each person rode at least one of these attractions. Using a Venn diagram, find
how many people rode:
a both attractions b the ferris wheel but not the roller coaster.
8 There are 46 shops in the local mall. 25 shops sell clothes, 16 sell shoes, and 34 sell at least one of
these items. With the aid of a Venn diagram, determine how many shops sell:
a both clothes and shoes b neither clothes nor shoes c clothes but not shoes.CIU() 1() (^6) () 14
() 5
RO
U
() 7
() (^16) () 11
() 14
backstroke but not freestyle
IGCSE01
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_02\071IGCSE01_02.CDR Friday, 12 September 2008 11:09:04 AM PETER