Practice Paper 01 Set
1. Which of the following are sets? Justify your answer
(a) The collection of all months of a year beginning with the letter A.
(b) The collection of best Indian cricketer.
(c) The collection of most difficult question in Math.
(d) The collection of prime numbers less than 50.
(e) The collection of all Indian women football player.
2. Write the following sets in roster form.
(a) A = {x: x is a natural number less than 9}
(b) B = {x: x is a two digit natural number such that the sum of its digit is 7}
(c) C = {x: x is a prime number which is a divisor of 24}
(d) D = Set of all letters in the word Mathematics
(e) P = Set of all letters in the word Theory
3. Write the following sets in the set-builder form.
(a) {2, 4, 8, 16, 32}
(b) {-1, 1, 3, 5, 7}
(c) {4, 8, 12, 16, 20}
(d) {2, 4, 8, 16, 32}
(e) {1, 7, 17, , 31, 49}
4. List all the elements of the following sets.
(a) A = {x: x is an integer, -1/4 < x < 9/4}
(b) B = {x: x is an odd natural number}
(c) C = {x: x is a vowel in English alphabet}
(d) D = {x: x is an odd number less than 20}
(e) E = {x: x is a letter in word "BEAUTIFUL"}
5. Which of the following are examples of the null set?
(a) Set of odd natural numbers divisible by 2.
(b) Set of even prime numbers.
(c) Set of prime number less than 2.
(d) {x: x is an integer, 7<x<6}
(e) Set of even number divisible by 3.
6. Which of the following sets are finite or infinite?
(a) The set of months of a year.
(b) {1, 2, 3 …}
(c) The set of lines which are parallel to the x-axis.
(d) The set of all prime numbers less than 100.
(e) The number of lines drawn from a point.
7. In the following, state whether A = B or not.
(a) A = {a, b, c, d}; B = {d, c, b, a}
(b) C = {4, 8, 12, 16}; D = {8, 4, 16, 18}
(c) S = {a, e, i, o, u}, T = {x: x is a vowel in English alphabet}
(d) A = {2, 4, 6, 8, 10}, B= {x: x is even numbers less than 100}
(e) A = {10, 20, 30, 40, 49}, C={x: x is a multiple of 5}
8.Write down all the subsets of the following sets:
(a) {a}
(b) {a, b}
(c) {1, 2, 3}
(d) {}
(e) {0, 1,2,3,4}
9. Write the following as intervals:
(a) {x: x ? R, –4 < x = 6}
(b) {x: x ? R, –12 < x < –10
9. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(a) A n B
(b) B n C
(c) A n C n D
(d) A n C
(e) B n D
10. If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
(a) A n B
(b) A n C
(c) A n D
(d) B n C
(e) B n D
(f) C n D
11. Which of the following pairs of sets are disjoint?
(a) {1, 2, 3, 4} and {x: x is a natural number and 4 = x = 6}
(b) {a, e, i, o, u}and {c, d, e, f}
12. If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(a) A – B
(b) A – C
(c) A – D
(d) (B - C)'
(e) (A U C)'
13. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
14. Let U = {1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, and C = {3, 4, 5, 6}. Find
(a) A’
(b) B’
(c) (A U C)’
(d) (B - C)'
(e) (A – B)'
14. If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(a) A = {a, b, c}
(b) B = {d, e, f, g}
15. Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(a) {x: x is an even natural number}
(b) {x: x is an odd natural number}
(c) {x: x is a positive multiple of 3}
(d) {x: x is a prime number}
16. If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(a) (A U B)’ = A’∩B’
(b) (A n B)’ = A’ U B’
17. Draw an appropriate Venn diagram for each of the following:
(a) (A U B)’
(b) A’ n B’
(c) (A n B)’
(d) A’ U B’
18. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A’?
19. If A and B are two sets such that n(A) = 23, n(B) = 52 and n(A∪B) = 70. Find n(A∩B).
20. In a group there are 650 people, 360 speaks Tamil and 420 can speak Hindi. How many people can speak both Tamil and Hindi?
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