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# F4 03 Sets

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### F4 03 Sets

1. 1. 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 A B 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: …………………. 12
2. 2. 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: …………………. 13
3. 3. ppr maths nbk 8. The shaded region in the Venn diagram below is ξ A B 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: ………………… 14
4. 4. 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 Q •1 R •2 •3 •7 •4 •6 •5 •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 M R 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 10 B 14 C 23 D 25 15
5. 5. ppr maths nbk 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 F B ξ E G E G F C ξ D ξ G F E E 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. X Y Z I II III IV V DIAGRAM 3 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 16
6. 6. ppr maths nbk 6. Diagram 4 is a Venn diagram, with the universal set ξ = A ∪ B ∪ C. A B I II IV V III 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. A‫ ∩ י‬B ∩ C B A‫ ∩ י‬B‫ ∩ י‬C C. ( A ∩ B )‫ ∩ י‬C D. A ∪B ∩ C 17
7. 7. ppr maths nbk 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. ξ A B 30 50 X 20 40 30 Y C A. 30 B. 40 C. 50 D. 60 18
8. 8. ppr maths nbk 10. P Q 4 x 2x 5 1 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. 4 B. 5 C. 6 D. 7 19
9. 9. 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 20
10. 10. ppr maths nbk 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 21
11. 11. ppr maths nbk 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 B .9 .2 .4 .5 .10 .8 .7 .6 C DIAGRAM 8 b. ξ .c A .i B .d .f .g .a C .e .b .h DIAGRAM 9 i) n(A∩C∪B) ii) n(A’∪B) 22
12. 12. ppr maths nbk 5. ξ M 6 P 1 N 3 2 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) ' 23
13. 13. 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 (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’). 24
14. 14. ppr maths nbk 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 25
15. 15. 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: (a) P ∩ Q’ ξ P Q R DIAGRAM 1 (b) ( P ∩ Q’) ∪ R ξ P Q R DIAGRAM 2 26
16. 16. 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 K L 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 27
17. 17. 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 B C DIAGRAM 7 (b) Set C ∩ B’ A B C DIAGRAM 8 (c) set ( B ∪ C )’ ∩ A A B C DIAGRAM 28
18. 18. 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 29