Question1. Write the following sets in roster form: 1. A={z: z=3x-8, x W and x<5} 2. B={x: x is an even prime number} 3. C={x: x >0 and x is a multiple of 3 less than 100} Question2. Write the following in set builder form: 1. A={1,4,9,16,25} 2. B={ } 3. C={Arctic, Atlantic, Indian, Pacific, Southern } Question3. Show that, {0} and 0 are all different. Question4. Fill in the blanks: 1. Every set is a subset of 2. is a subset of every set. 3. All equal sets are sets. 4. If A is subset of B and B is subset of A then Question5. Solve the following equations for x where x is a whole number: 1. 8x-24=0 2. x+1=0 Question6. If U = {2,4,6,8,10,11,15} A={4,6,10}, B={10,11} and C={2,8,15} then find A, B, C, n(a ), n(b ) Question7.How many proper subsets in all are there if a set contains (a) 7 elements (b) 4 elements Question8.Define the following with example: 1. Null set 2. Subset 3. Disjoint sets 4. Singleton set Copyright 2011-12 Educomp Solutions Ltd. Page 1 of 5
Question9.State the cardinal number of the following: 1. A={A quadrilateral having five sides} 2. B={x: x I and -4 2} 3. C={set of letters in the word MEDITERRANEAN} Question10. Let A= {a,b,c,d,e}. List the subsets of A as directed. 1. All subsets with two elements. 2. 3. 2.{a,b,c},{a,c,d},{a,b,d},{a,b,e},{a,c,e}{a,d,e},{b,c,d},{b,c,e},{c,d,e}, {b,d,e} 3.{a,b,c,d},{a,c,d,e},{b,c,d,e},{a,b,d,e} and {a,b,c,e} Question11. Which of the following pair of sets is disjoint? Justify. 1. A={x: x=n 3, n N and n 4} B={x: x N and 2 } 2. A={x: x is a square number less than 20} B= {1,9,25} Question12. A true or false. 1. {0} {2,3} 2. {} {0} 3. 0 {} 4. {2,4,6} {x: x is an even number} 5. {l,m,n} 6. {x:x is a square} {x:x is a rectangle} Copyright 2011-12 Educomp Solutions Ltd. Page 2 of 5
Question13. State whether the following pair of sets are equal or equivalent: 1. A={x: x is a consonant in STANDARD} B={x: x is a consonant in STRAND} 2. A={x: x N and 1 } B={x: x=n+1 and 0 9} 3. A={x: x is a vowel in BLUE} B={x: x is a vowel in YELLOW} Question14. Define universal set and explain with an example. Question15. Classify the following sets as finite or infinite sets: 1. A={set of all river in the world} 2. B={ set of negative integers less than zero} 3. C={x: x is a prime number} 4. D={x: x N and x>10} 5. E={x: x is a continent} Question16.If U = set of first 20 even numbers then list the following subsets: 1. Set of multiples of 9 2. Set of prime numbers 3. Set of numbers divisible by 7 Question17. State whether the sets are empty, singleton, finite or infinite. 1. A={x: x is a fraction between 5 and 6} 2. B={x: x is a month having more than 31 days} 3. C={set of stars in the sky} 4. D={x: x W and x<1} 5. E={x: x I and -4<x<-2} Question18. Suggest the universal set for the following: 1. A={violet, indigo, red} 2. B={x: x is a consonant} 3. C={1/11,1/10, 1/9, 1/3} 4. D={5,10,15,20} Copyright 2011-12 Educomp Solutions Ltd. Page 3 of 5
Question19. Let A= set of alphabets in the word READ. List all the subsets of set A. Question20. Define complement of a set with example. Answers:- A1. 1. A={-8,-5,-2,1,4} 2. B={2} 3. C={3,6,9,..,99} A2: 1. A={x: x=y 2, y N and y<6} 2. B={x: x= 12, n N and n 16} 3. C={x:x is an ocean} A4. 1. itself; 2. Null set; 3. Equivalent; 4. A=B A5. 1. 3 ; 2. A6. A ={2,8,11,15}, B ={2,4,6,8,15}, C ={4,6,10,11}, n(a )=4 and n(b )=5 A7. (a)127 (b)15 A9.1.n(A)= zero; 2. n (B)=7; 3. n(c)=8 A10. 1. {a, b },{a, c }, {a, d}, {a, e}, {b, c }, {b, d }, {b, e}, {c, d}, {c, e} and {d, e } A11. 1.A= {1, 8, 27, 64} and B={2,3,4,5,6} therefore Disjoint sets 2. A= {1, 4, 9, 16} and B={1,9,25}.since 1 and 9 are common thus not disjoint. Copyright 2011-12 Educomp Solutions Ltd. Page 4 of 5
A12. 1. False 2. True 3. False 4. True 5. False 6. True A13.1. Equal sets, 2. Equal sets, 3. Equivalent sets. A15. 1. Finite, 2.infinite, 3. Infinite, 4. Infinite, 5.finite A16.1. A={18,36}; 2. B={2}; 3. C={14,28} A17. 1. Infinite, 2. Empty, 3. Infinite 4. Singleton 5. singleton A18. 1. {set of colours in a rainbow}, 2. {x: x is an alphabet}, 3. {x: x is a fraction} 4. { x: x is a multiple of 5} A19.{R},{E},{A},{D},{R,E},{R,A}{R,D},{E,A},{E,D},{A,D},{R,E,A}, {R,E,D},{E,A,D},{R,A,D}, {R,E,A,D} and Copyright 2011-12 Educomp Solutions Ltd. Page 5 of 5