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0% found this document useful (0 votes)
42 views12 pagesSets
O LEVEL Classified
Uploaded by
Nadeem AhmadCopyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
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Unit :
Sets and Venn Diagrams
10
1. (@) On the Venn diagram in the answer space, shade the set (A 0B) UC
B
c
(b) The Universal set is the set of all positive integers and P = {x x < 10}
Complete the statement: P= fx. } (12000/1/7)
2
(a) A, B and C are subsets of the universal set e. BU A = B and BC = ®, Illustrate this on
the Venn diagram in the answer space
|
Co
(b) In a group of people. 15 drink tea, 28 drink coffee. 12 drink both tea and coffee and 6
drink neither tea nor coffee. By drawing a Venn diagram, or otherwise, find the total
number of people in the group. (Int Exam N2000/1/10)
eee
(1.2. 3,4.5,6.7,8.9, 10.11}
: x is an even number)
(x: xis a multiple of 3}
(a) Draw a Venn Diagram to illustrate these sets, indicating the members of each subset
(b) (i) A number m is chosen at random from ¢. Find the probability that
Vea) ned,
Ab) ned’,
Me) near.
(a) n=14
(ii) second number mis chosen at random from the complete set ¢. Find the
probability that the sum of » and m is 18, (32001/2/4)
(10) 1 4. -(a)_On the Venn Diagram, shade the set
| (PUR)OQ.
(b) Express in set notation, as simply as
\ possible, the set shaded in the Venn
' Diagram.
(c
There are 27 people in a restaurant. Of these, 10 eat fish, 15 eat meat and 9 eat neither fish
‘nor meat.
Using a Venn Diagram, or otherwise, find the number of people in the restaurant who eat
fish but not meat (Int'l Exam N2001/1/20)
There are 50 people on a tour. One day. 26 people went on the morning cruise and 29 to the
evening barbecue. Using Venn diagrams, or otherwise, answer the following questions.
(a) It was thought that 4 people went to both events and |
person to neither. Explain why this was not possible
\ (b) Find the least number and the greatest number of people who could have gone to both
events. (3202/19)
6. (a) Onthe Venn diagram in the answer space,
shade the set (4G B) AC
| @) e= bx xis an imeger and 4 5}
Q={x:x<3}
(@) Find the value of n(PUQ).
ii) List the elements of P’OQ’ (2007/1/9)
13. (a) Express, in set notation, as simply as possible,
the subset shaded in the Venn diagram.
6
(b) It is given that n(%)= 40, n(P)=18, A B
n(Q)=20 and n(PQ)=7 es
- ee)
@) n(PUQ), (os
Gi) n(P'AQ’.
(N2007/19) ,
14. Mary has 50 counters.
Some of the counters are square, the remainder are round.
There are 11 square counters that are green.
There are 15 square counters that are not green.
Of the round counters, the number that are not green is double the number that are
green
By drawing a Venn diagram, or otherwise. find the number of counters that are
(round, )
(i) round and green,
(iii) not_green. (s2008/2/5a) hade the’ set PUQ’:
15. (@ On the Venn diagram shown in the answer space, sha¢ o
z|
(©). There are 27 children, in a, class.
Of these children, 19 own a bicycle,
Using Sen diagram, or otherwise, find the number of children who own a bicycle
5008/1
but not a scooter. (2008/14)
15 own a scooter and 3 own neither a bicycle
#={1,2,3,4,5}, ; \ a
A=(1,2,3}, a
B={5}, |
C=(3,4} |
List the elements of ;
@ auc
Gi) BNC.
(b) A group of 60 children attend an after school club.
Of these, 35 children play football and 29 play hockey.
3 children do not play either football or hockey.
By drawing a Venn diagram, or otherwise, find the number of children who play only
hockey. (420091118)
17. (f= {1,2,3,4,5,6,7,8, 9,10, 11,12, 13,14, 15} '
L={x:x is an odd number} i
M ={x:x isa multiple of 3} |
Write down
@ La,
0) Liam.
(GA number m is chosen at random from ¢
Find the probability that neLUM.
(10) 6 (b) In a survey, a number of people were asked "Do. you own a.car?" and "Do. you own
a bicycle?", The Venn diagram shows the set C of car owners and the set B of
bicycle owners.
The letters p, q and x are the numbers of people in each subset.
11 people owned neither a car nor a bicycle.
A total of 66 people owned a car.
4 times as many people owned a car only as owned a bicycle only.
(Write down expressions, in terms of x, for
@ ep
b) g
(i) A total of 27 people owned a bicycle. Calculate
@ xs
(b) the total number of people who were in the survey. (N2009/2/4)
(se I, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12,13,14,15,16}
Az={x:x is a multiple of 3}
B={x:x isa factor of 24}
C = {x:x is an odd number}
A) Find
(a) (8),
(b) (AU BUC)
aa A number, k, is chosen at random from 2
Find the probability that ke 47.8. (20102/5e)
19. The Venn diagram shows the sets 6, P, O and R
(12,3, 4, 5. 6.7. 8. 9, 10}
Va Find the value of n(Qu R).
/ ) List the elements of the set P’A(QUR).
(©) One element is chosen at random from &.
Write down the probability that this element belongs to (PAQ)U(PAR).
(N2010/1/11)
(10) 7 20.(a) On the Venn diaigram, shade the set’ A BAC. at stoge
(b) = 2, 3, 4, 5, 6, 7, 8 9, 10}
P = {x:x is a prime number}
O={x:x25}
@ Find the value of n(PQ).
(ii) List the elements of PUQ’.
21, The Venn diagram shows the Universal set and the set B.
A and C are two sets such that
AUB=B, ANB#B, ANC=@ and BNC#.
Draw the sets A and C in the Venn diagram.
€
2. (@) G=( x: is an integer, 2