ASSIGNMENT – 1 MATHEMATICS SETS
01. Write the set of all integers 'x' such that –2 < x – 4 < 5.
02. Write the set {1, 2, 5, 10} in set builder form.
03. If A = {x : x2 < 9, x Z} and B = {–2, –1, 1, 2} then find whether sets A and B are equal or not.
04. State true/false :
A = {p, q, r, s}, B = {p, q, r, p, t} then A B.
05. State true/false :
A = {p, q, r, s}, B = {s, r, q, p} then A B.
06. State true/false : [4, 15) [–15, 15]
07. Find A B if A = {x : x = 2n + 1, n 5, n N} and B = {x : x = 3n – 2, n 4, n N}.
08. Find A – (A – B) if A = {5, 9, 13, 17, 21} and B = {3, 6, 9, 12, 15, 18, 21, 24}
09. Write the following sets in set-builder form :
(i) A 1,4,9,16,.......
(ii) A 5,9,13,17,21,.......
(iii) A 14,21,28,35,42,.....,98
(iv) A 3,6,9,12,.....
10. Write the following sets in tabular form (roster form) :
(i) A = {x : x is a natural number and 5 x 6}
(ii) B x : x 2 x 4 0
(iii) C x : x 2n 1 20 and n N
n
(iv) D x : x ,n 5,n N
n1
11. Match each of the sets on the Column-1 described in the roaster form with the same set on the
Column-2 described in the set-builder form :
Column-1 Column-2
(i) {H, A, R, I, B} (a) {x : x is a natural number and is a divisor of 18}
(ii) {L, I, T, E} (b) {x : x is a letter of the world BIHAR}
(iii) {1, 2, 3, 4, 6, 12} (c) {x : x is a letter of the world LITTLE}
(iv) {1, 2, 3, 6, 9, 18} (d) {x : x is a natural number and is a divisor of 12}
12. Determine the empty sets and, singleton set in the following sets :
(i) A = {x : x2 = 2, x is a rational number} (ii) B = {x : x > 0 and x2 = 25}
(iii) C = {x : x3 + 1 = 0 and x is an integer
13. Let A and B be two finite sets such that n(A – B) = 15, n(A B) = 90, n(A B) = 30.
Find n(B)?
15. Find the number of different subsets that can be formed from the set A = {4, 5, 6}.
16. If S = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 4, 6, 8}, B = {1, 3, 5, 7, 8}, C = {1, 2, 8, 9}. Then verify that
(i) A B C A B A C (ii) A C A C
17. Find number of integers in the following intervals
(A) (–5, 9] (B) [–10, 12] (C) (–7, 12)
18. If universal set is R and sets A, B & C are given as A = [–5, 20], B = [5, 100), C = (–10, 30) then find
(A) A B (B) B C (C) A ' C (D) A B C
(E) B' C' (F) A ' B C
19. Find number of (a) real numbers
(A) rational numbers (B) rational numbers (C) integers in set
A [ 5,5) 20,30 40,50.
20. The set of intelligent students in a class is-
(A) a null set (B) a singleton set
(C) a finite set (D) not a well defined collection
21. The set A = {x : x R, x = 16 and 2x = 6} is
2
(A) Null set (B) Singleton set
(C) Infinite set (D) not a well defined collection
22. If A = {x : –3 < x < 3, x Z} then the number of subsets of A is –
(A) 120 (B) 30 (C) 31 (D) 32
23. Which of the following are true ?
(A) [3, 7] (2, 10) (B) (0, ) (4, )
(C) (5, 7] [5, 7) (D) [2, 7] (2.9, 8)
24. The number of subsets of the power set of set A = {7, 10, 11} is
(A) 32 (B) 16 (C) 64 (D) 256
25. Which of the following sets is an infinite set?
(A) Set of divisors of 24 (B) Set of all real number which lie between 1 and 2
(C) Set of all human beings living in India. (D) Set of all three digit natural numbers
26. Let A = {x : x R, –1 < x < 1} , B = {x : x R, x 0 or x 2} and A B = R – D, then the set D is
(A) {x : 1 < x 2} (B) {x : 1 x < 2} (C) {x : 1 x 2} (D) {x : 1 < x < 2}
27. If A = {2, 3, 4, 8, 10}, B = {3, 4, 5, 10, 12}, C = {4, 5, 6, 12, 14} then (A B) (A C) is equal to
(A) {3, 4, 10} (B) {2, 8, 10} (C) {4, 5, 6} (D) {3, 5, 14}
29. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 5}, B = {6, 7}, then A Bis
(A) B (B) A (C) A (D) B
30. If A = {x : x = 4n + 1, n 5, n N} and B {3n : n 8, n N}, then A – (A – B) is :
(A) {9, 21} (B) {9, 12} (C) {6, 12} (D) {6, 21}
ANSWER KEYS
1. {3, 4, 5, 6, 7, 8}
2. {x : x is a natural number and a divisor of 10}
3. Not equal sets
4. False 5. True 6. True
7. {1, 3, 4, 5, 7, 9, 10, 11}
8. {9, 21}
9.
(i) A x : x n2 & n N
(ii) A x : x 4n 1,n N
(iii) A x : x 7n,n N & 2 n 14
(iv) A x : x 3n,n N
10. (i) A = {6}
1 17 1 17
(ii) B ,
2 2
(iii) C 1,3,5,7,9,11,13,15,17,19
1 2 3 4
(iv) D , , ,
2 3 4 5
11. (i) –(b), (ii) –(c), (iii) – (d) (iv) – (A)
12. (i) (ii) singleton set {5} (iii) singleton set {–1}
13. 75 15. 8
17. (A) 14 , (B) 23, (C) 18
18. (A) [–5, 100), (B) [30, 100),
(C) 10, 5 20,30
(D) [5, 20] (E) ,5 [30, )
,
(F) 10, 5 [5,30)
19. (A) infinite, (B) Infinite, (C) 30
20. (D) 21. (A) 22. (D) 23. (A) 24. (D) 25. (B)
26. (B) 27. (A) 29. (B) 30. (A)
