1

1 The Venn diagram in the answer space shows sets P, Q and R such that the universal set,

M

LK

3

5x

2

4x + 37

5

8

.

On the diagram in the answer space, shade

(a) the set

Q

P

(.

(b) the set ( P ( Q )( ( R .

[3 marks]

Answer :

R

Q

P

=

x

(a) (b)

2If

x

= {x : 1 x 10 , x is an integer}

E = {x : x is a multiple of 4}

F = {x : x is a factor of 20}

(a) List all the elements in set E,

(b) Find

()

nEF

.

[3 marks]

3. The Venn diagram in the answer space shows set P, set Q and set R with the universal set ( = P ( Q ( R.

On the diagram in the answer space, shade

(a)P ( Q ( R

(b)P ( ( Q ( R) (

[3 marks]

Answer:

(a)

(b)

4. Diagram 1 shows an incomplete Venn diagram that represents the number of students from a class of 30, according to the subjects they have studied. Each student studied at least one of the three subjects Physics, Chemistry and Biology.

Given the universal set, ( = P ( C ( B,

P = {students who studied Physics}

C = {students who studied Chemistry}

B = {students who studied Biology}

DIAGRAM 1

20 students studied Chemistry and 12 students studied Biology. Based on this information, find

(a)the number of students who studied Chemistry and Biology but not

Physics.

(b)the number of students who studied Biology only.

(c)the number of students who studied Physics.

[4 marks]

5. (a) Given that ( = { x: x is an integer and 7 x 15},

A = { x: x is a multiple of 3 },

B = {x : x is an odd number} and

C = { x: 10 x 13 }.

(i) List the elements of the set C ( .

(ii) Find n(A (B).

(iii) List all the possible subsets of set A.

(iv) Find the element x such that x ( (B ( C () and x ( A. [7 marks]

(b)Given that n(() = 50. G and H are two sets for which n( G ( H) = 6, n(G) = 18 and n(H) = 14.

(i) Draw a Venn diagram to represent the relationship between sets G and H and write the number of elements in each region.

(ii) Find n(G ( H)(. [3 marks]

(c) On the Venn diagram in the answer space, draw a set N such that N ( L and N ( M = (. [2 marks]

Answer:

(b)(i)

(c)

6 The Venn diagram in the answer space shows the universal set (, sets P, Q and R.

The universal set ( = P ( Q ( R.

On the diagram in the answer space, shade the region for

(a) P ( Q,

(b) P ( ( Q ( R ).

[3 marks]

Answer:

(a)

(b)

7 The Venn diagram in the answer space shows sets J ,K and L.

In the answer space, shade

(a) J ( L

(b)(K ( L)( J

[3 marks]

Answer:

(a)

(b)

8. The Venn Diagram shows all the elements of sets K, L and M. Given that

.

M

L

K

=

x

(a) List all the members of

.

M

'

K

(b) Find

(

)

[

]

.

'

M

L

K

n

(4 marks )

9.The Venn Diagra, in the answer space below shows sets P , Q and R . Given that the universal set = P Q R . In the answer space, shade

(a) P R ,

(b) P R Q

[ 3 marks ]

Answers:

(a)

P R

Q

(b)

P R

Q

10. The Venn diagram in the answer space shows sets P, Q and R such that the universal

set,

.

R

Q

P

=

x

On the diagram in the answer space, shade

(a) the set

Q

P

'

,

(b) the set

R

Q

P

)

'

(

Answer: [3 marks]

(a) b)

13. The Venn diagram in the answer space shows sets A, B and C. On the diagram provided in the answer spaces, shade

(a) the set

'

B

A

,

(b) the set

'

C

B

A

.

[4 marks]

Answer:

(a)

14. (a) Given

=

E

{x : x is an odd number},

F = { x : x is an even number} and

G = { x : x is a prime number}.

(i) Simplify

F

E

.

(ii) List the elements of

.

G

F

(iii) Draw a Venn diagram to represent the relationship between sets E, F and G.

[6 marks]

(b) Given

=

x

{ x : x is an integer,

22

10

x

},

P = { x : x is a prime number},

Q = { x : x is a perfect square} and

R = { x : x is a number of which the sum of its digits is more than 6}.

(i) List the elements of set R.

(ii) Simplify

.

R

Q

(iii) Find the value of

(

)

'.

R

Q

P

n

[6 marks]

15.

i) The Venn diagram shows the number

of elements in each region of set K, set L and

set M. The universal set

.

M

L

K

=

x

It is

given that

)'

(

)

(

M

K

n

M

n

=

.

Find the value of x.

ii) If the universal set

,

20

5

:

{