Sets

ppr maths nbk CHAPTER 3: SETS EXERCISE 2 1.

Given P = { 1,4, 6, 8, 9} , Q = { 3,4, 6, 7, 10} , R = { 2, 3,4, 8,9 } List the elements in the intersection of the following set. P ∩Q∩ R =

ANSWER: …………………. 2

Given ξ = A ∪B ∪ C . Shade the region represented by the set (A ∪ B) ∩ C ANSWER: ξ

B

A

C

3.

Determine the union of the following pairs of sets. A = { x : x is a factor12 } B = { x : x is a multiple of 4 less than 16 }

ANSWER: …………………. 4.

Given that the universal set ξ = { x : 14

≤ x ≤ 27 , x are integers }.

Set A = { x : x are even numbers } Set B = { x : x are perfect square numbers } Find the complement of the following union of sets A and B.

ANSWER: ………………….

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ppr maths nbk 5.

Shade the complement of the set, (A ∪ B ∪C ) ANSWER: A

ξ B

C

6.

Given universal set ξ = P U Q U R such as Set ξ = { x : 4 ≤ x ≤ 14 , x are integers } Set P = { x : x are multiples of 6 } Set Q = { x : x are odd numbers } Set P U R = { x : x are multiples of 2 } and P ⊂ R. Find n ( P‫ ∩ י‬R ).

ANSWER: …………………. 7.

Given ξ = { x: ≤ 2 ≤ x ≤ 10 , x are integers } , F = { 4,10 } and G = { Prime numbers } List the elements for set ( F ∪ G)‫י‬

ANSWER: ………………….

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ppr maths nbk 8.

The shaded region in the

Venn diagram below is

ξ B

A

C

ANSWER: …………………. 9.

Given universal set : ξ = { x : 5 ≤ x ≤ 14, x are integers } P = { x : x are even numbers } Q = { x : x are prime numbers } The elements in set P ∪ Q are

ANSWER: …………………. 10.

The diagram shows the universal set ξ , set A and B. The shaded region in the diagram below is represented by the set

ξ

A

B

ANSWER: …………………

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ppr maths nbk CHAPTER 3: SETS DIAGNOSTIC TEST 1

Diagram 1 is a Venn diagram which shows the elements of the sets P, Q and R. P •1

R

•2

•4

•6

•5

Q •3

•7

•2 DIAGRAM 1 If the universal set , ξ = P ∪ Q ∪ R , then set P′ ∪ R′ ∩ Q is A {5,7} B {2,6} C {2,3,6} D {2,3,6,7} 2

Diagram 2 represents a class of 40 pupils. Set M = {Pupils who play tennis} and set R = { Pupils who play badminton} . ξ R

M

DIAGRAM 2 Given that n (M) = 19 , n (M ∩ R ) = 9 and the number of pupils who do not play either game is 7, find the number of pupils who play badminton. A B C D

10 14 23 25

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3

Given that the universal set ξ = E ∪ F ∪ G , G ⊂ F and E ∩ G ≠ ∅ , the Venn diagram that represents these relationships is A

C

ξ

B

F

E

ξ

E

G

ξ

D

G

E

G F

ξ E

F

F G

4

Given that the universal set ξ = {x: 1 ≤ x ≤ 10, x is an integer}, set L ={1,3,5,9}, set M = {x: x is a perfect square} and set N = {x: x is a multiple of 3}, n ( L ∪ M ∩ N ′ ) is A 0 B 2 C 3 D 8

5

Diagram 3 is a Venn diagram with the universal set ξ = X ∪ Y ∪ Z. Y

X I

II

III

Z IV

V

DIAGRAM 3 The set X ∪ ( Y ∩ Z ) is represented by the regions A B C D

I,V I , II , IV I , III, V I , II , IV , V 16

ppr maths nbk 6.

Diagram 4 is a Venn diagram, with the universal set ξ = A ∪ B ∪ C.

A I III

IV

II

B V

C Diagram 4 The set A ∩ C , is represented

by

regions

A. II, IV B. I, II, IV C. I, II, III D. II, III, IV 7.

The shaded region represents the set

A B

C

A. B C. D.

A‫ ∩ י‬B ∩ C A‫ ∩ י‬B‫ ∩ י‬C ( A ∩ B )‫ ∩ י‬C A ∪B ∩ C

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Given that the universal set ξ = { x : 1 ≤ x < 20 , x is an integer} The set E = { Perfect square numbers less than 30 } F = { Multiples of 4 less than 20 } List the element E ∩ F‫י‬

8.

A. B C. D. 9.

{ 4,16 } { 1, 9 } { 8, 12 } { 1, 4, 8, 9, 12, 16 }

Diagram below shows the number of clients in three banks. Given ξ = A ∪ B ∪ C and n(ξ) = 300. The number of clients for Bank B is more than those in Bank A by 40 people. Find the value of Y.

ξ A 50

30 40 Y

A. B. C. D.

B

X

20 30 C

30 40 50 60

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ppr maths nbk 10. Q

P x

4 1

2x

5 3 6 R

The Venn diagram shows the number of elements in set P ,Q and R. Given universal set , E = P U Q U R and n(E) = 40 . Find the value of x. A. B. C. D.

4 5 6 7

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ppr maths nbk CHAPTER 3: SETS EXERCISE 1 (Paper 2) 1. The Venn diagram shows set A, B and C. The universal set ξ = A ∪ B ∪ C . Shade on separate Venn diagrams in Diagram 1 and Diadram 2, the region that represents each set given below.

a.

A∪ B

A C B

DIAGRAM 1 b.

B’ ∩ C A C B

DIAGRAM 2 2. The Venn diagram shows sets P, Q and R. Shade the region in the Diagram 3 and Diagram 4 which represents a. P Q R’ P

Q

R

DIAGRAM 3

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P

b. P ∪ Q ∩ R '

Q

R DIAGRAM 4 3. The Venn diagram shows sets E, F and G. The universal set ξ = E ∪ F ∪ G . Shade the region that represent each of the following sets in the Diagram 5, Diagram 6 and Diagram 7. a.

F’ ∩ G E G

F

DIAGRAM 5 b. (F ∪ G ) ' ∩ E E G

F

DIAGRAM 6 c.

F ∪ (E ∩ G ' ) E G

F DIAGRAM 7

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4. The Venn diagram shows the relationship among sets A, B, C and ξ . Find the number of elements in the Diagram 8 and Diagram 9. a. i) n(A∪B)’ ii) n(A∩B∩C’)

ξ .3 A

.1 .2 .4 .8

.9

B .5

.10

.7 .6

C

DIAGRAM 8 b.

ξ B

.d .e

.f .g

A

.c C .b

.i

.a .h

DIAGRAM 9 i) ii)

n(A∩C∪B) n(A’∪B)

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ppr maths nbk 5.

ξ M

6 N

3

2

P

1 5 7

DIAGRAM 10 The Venn diagram in the Diagram 10 shows the sets M, N and P in the universal set ξ . The number of elements in each set is shown by the number in each region. Find a. n ( N ∪ P)

b. n ( M ∩ P) c. n ( N ∪ P) '

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ppr maths nbk CHAPTER 3: SETS EXERCISE 2

1. Given the universal set, ξ = {x:20≤x≤35, where x are integers}, A= {multiples of 5}, B= {x:x are numbers where one of the digit is 0} and C= {x:x are numbers where the tens digit > the units digit}. (a) List the elements of set B and C. (b) Find n(A∪B). (c) Find n(A∩C). 2. Given set R = {2,4}, S = {1,2,3,4,5,6} and T = {0, 2, 3, 4, 5, 6, 7, 8, 12}. The universal set, ξ = R∪S∪T. (a) Draw a Venn diagram to show the relationship amongst R, S and T. (b) List the elements of S ∩ T (c) Find n(R’∩T). 3. Shade the following related region in Diagram 1 and Diagram 2. (a) P∩Q P

(b) P'∩Q∩R Q

R DIAGRAM 1

P

Q

R DIAGRAM 2

4. Given the universal set, ξ = {x:20≤x≤32, x are integers} set P = {x:x are multiples of 3}, set Q= {x:x are factors of 100} and set R= {x:x are numbers where the sum of its digits is 5}. Find (a) Set P, (b) Set Q, (c) n(Q∩R’).

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5. The Venn diagram below shows set P, Q and R. On Diagram 3 and Diagram 4 provided, shade (a) P’∩Q∩R’ P

Q

R

DIAGRAM 3 (b) P∪Q’∪R

P

Q

R DIAGRAM 4

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ppr maths nbk CHAPTER 3: SETS DIAGNOSTICS TEST

1.

The Venn diagram in the answer space shows sets ξ , P, Q and R. ξ = P ∪ Q ∪ R. On the Diagram1 and Diagram 2 in the answer space, shade the set [ 3 marks] Answer: P ∩ Q’

(a)

ξ P R

Q

DIAGRAM 1

( P ∩ Q’) ∪ R

(b) ξ

P Q R

DIAGRAM 2

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ppr maths nbk

2.

The Venn diagram in the answer space shows sets J, K and L. ξ = J ∪ K ∪ L. On the Diagram 3 and Diagram 4 in the answer space, shade the set [ 3 marks] Answer: (a)

(J∪L)∩K J

L

K

DIAGRAM 3 (b)

J ∩ ( K’ ∪ L) J

K

L

DIAGRAM 4 3.

The Venn diagram in the answer space shows sets P, S and R. On the Diagram 5 and Diagram 6 in the answer space, shade the set [ 3 marks] Answer: (a)

P ∩ S’ P

R S

DIAGRAM 5

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ppr maths nbk

(b)

( P ∩ R )’ ∩ S’ P R

S

DIAGRAM 6 4.

The Venn diagram in the answer space shows sets A, B and C. ξ=A∪B∪C On the Diagram 7, Diagram 8 and Diagram 9 in the answer space, shade the [ 3 marks] Answer: (a) set A ∪ B A C

B

DIAGRAM 7 (b)

Set C ∩ B’ A B

C

DIAGRAM 8 (c)

set ( B ∪ C )’ ∩ A A B

C

DIAGRAM

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ppr maths nbk

5.

The incomplete Venn diagram in the Diagram 10 shows sets ξ , J and K. Set L satisfies the following conditions L⊂ξ L ∩ J ≠ ∅ and L ∩ K ≠ ∅ L ⊂ J = ∅ and L ⊂ K = ∅ Draw the set L in the Diagram 10 in the answer space. [ 3 marks] Answer: ξ J

K

DIAGRAM 10

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