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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:

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: ………………….

ξ A B

C

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

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 ( Pי ∩ R ). 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: ………………….

ξ A

B

C

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8. The shaded region in the Venn diagram below is

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

ANSWER: …………………

A Bξ

A B

C

ξ

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CHAPTER 3: SETS DIAGNOSTIC TEST

1 Diagram 1 is a Venn diagram which shows the elements of the sets P, Q and R. 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 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 10 B 14 C 23 D 25

• 6

• 1

• 4 • 5 • 7

• 2

• 2

• 3

P R

Q

M R

DIAGRAM 1

DIAGRAM 2

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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 ξ B ξ C ξ D ξ 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. The set X ∪ ( Y ∩ Z ) is represented by the regions A I , V B I , II , IV C I , III, V D I , II , IV , V

E F

G E G

F

E F

E F

G

G

X

Y Z

DIAGRAM 3

I II III IV V

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6. Diagram 4 is a Venn diagram, with the universal set ξ = A ∪ B ∪ 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. Aי ∩ B ∩ C B Aי ∩ Bי ∩ C C. ( A ∩ B )י ∩ C D. A ∪ B ∩ C

A

B

C

IIII II IV V

A

B

C

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8. 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 A. { 4,16 } B { 1, 9 } C. { 8, 12 } D. { 1, 4, 8, 9, 12, 16 } 9. 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.

A. 30 B. 40 C. 50 D. 60

30 50 X

302040

Y

AB

C

ξ

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10.

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. 4 B. 5 C. 6 D. 7

4 2xx

15

3

6

P Q

R

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CHAPTER 3: SETS EXERCISE 1 (Paper 2) 1. The Venn diagram shows set A, B and C. The universal setξ = CBA ∪∪ . Shade on separate Venn diagrams in Diagram 1 and Diadram 2, the region that represents each set given below. a. A B∪ DIAGRAM 1 b. B’ C∩ 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’ DIAGRAM 3

A

B

C

B

C

P Q R

A

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b. 'RQP ∩∪ DIAGRAM 4 3. The Venn diagram shows sets E, F and G. The universal set ξ = GFE ∪∪ . Shade the region that represent each of the following sets in the Diagram 5, Diagram 6 and Diagram 7. a. F’ G∩ DIAGRAM 5 b. (F ')G∪ E∩ DIAGRAM 6 c. '( GEF ∩∪ )

DIAGRAM 7

P

R

Q

E

F G

E

F G

E

F G

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4. The Venn diagram shows the relationship among sets A, B, C andξ . Find the number of elements in the Diagram 8 and Diagram 9.

a. i) n(A∪B)’ ii) n(A∩B∩C’)

ξ DIAGRAM 8 b. ξ

DIAGRAM 9

i) n(A∩C∪B) ii) n(A’∪B)

B A

C

.1

.2

.3

.4 .9

.7

.6

.5

.8

.10

B A

C .a

.c .b

.f

.g .d .e

.i .h

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5. ξ DIAGRAM 10 The Venn diagram in the Diagram 10 shows the sets M, N and P in the universal setξ . 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∪

M

N

P 6

3 2 1

5

7

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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 (b) P'∩Q∩R P Q P Q

R R

DIAGRAM 1 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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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: (a) P ∩ Q’ DIAGRAM 1 (b) ( P ∩ Q’) ∪ R DIAGRAM 2

ξ

ξ

P

Q R

P Q

R

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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 DIAGRAM 3 (b) 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’ DIAGRAM 5

J K L

P

S

R

J K L

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(b) ( 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 DIAGRAM 7

(b) Set C ∩ B’

DIAGRAM 8

(c) set ( B ∪ C )’ ∩ A

DIAGRAM

P

S

R

A

B C

A

B C

A

B C

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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: DIAGRAM 10

J K

ξ