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Class 11 | CBSE | MATHEMATICS
CHAPTER - 1 | SETS | EX: 1.1
FULLY SOLVED – EXERCISE 1.1 (SETS) written in a CBSE-exam–oriented teacher’s style, with clear justification, step-by-step logic
EXERCISE 1.1 — SOLUTIONS
1. Which of the following are sets? Justify your answer.
1. Which of the following are sets? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
✔ This is a set, because the collection is well-defined.
Months are: January, June, July.
(ii) The collection of ten most talented writers of India.
✘ This is not a set, because the term “most talented” is subjective.
(iii) A team of eleven best-cricket batsmen of the world.
✘ This is not a set, because “best” is not well-defined.
(iv) The collection of all boys in your class.
✔ This is a set, because membership can be decided clearly.
(v) The collection of all natural numbers less than 100.
✔ This is a set, because it is well-defined.
(vi) A collection of novels written by Munshi Prem Chand.
✔ This is a set, because the list is definite.
(vii) The collection of all even integers.
✔ This is a set.
(viii) The collection of questions in this chapter.
✔ This is a set, because the questions are fixed.
(ix) A collection of most dangerous animals of the world.
✘ This is not a set, because “most dangerous” is subjective.
2. Let A = {1, 2, 3, 4, 5, 6}
Insert ∈ or ∉ :
- 5 ___ A ---> 5 ∈ A
- 8 ___ A ---> 8 ∉ A
- 0 ___ A ---> 0 ∉ A
- 4 ___ A ---> 4 ∈ A
- 2 ___ A ---> 2 ∈ A
- 10 ___ A ---> 10 ∉ A
3. Write the following sets in roster form
(i) A={x:x is an integer and −3≤x<7}
\[ \begin{aligned} A &= \{x : x \in Z,\; -3 \le x < 7\} \\ A &= \{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6\} \end{aligned} \](ii) B={x:x is a natural number less than 6}
\[ B = \{1, 2, 3, 4, 5\} \](iii) Two-digit numbers whose digits sum to 8:
\[ C = \{17, 26, 35, 44, 53, 62, 71, 80\} \](iv) Prime divisors of 60:
\[ D = \{2, 3, 5\} \]
60=2²×3×5(v)Letters of TRIGONOMETRY (no repetition):
\[ E = \{T, R, I, G, O, N, O, M, E, T, R, Y\} \]
E={T,R,I,G,O,N,O,M,E,T,R,Y}(vi) Letters of BETTER:
\[ F = \{B, E, T, R\} \]
F={B,E,T,T,E,R}
Removing repetition:
4. Write the following sets in set-builder form
(i) {3, 6 ,9 ,12}
\[ \{x : x = 3n,\; n \in N,\; 1 \le n \le 4\} \](ii) {2, 4, 8, 16, 32}
\[ \{x : x = 2^n,\; n \in N,\; 1 \le n \le 5\} \](iii) {5, 25, 125, 625}
\[ \{x : x = 5^n,\; n \in N,\; 1 \le n \le 4\} \](iv) {2, 4, 6, ......}
\[ \{x : x = 2n,\; n \in N\} \](v) {1, 4, 9, ....., 100}
\[ \{x : x = n^2,\; n \in N,\; 1 \le n \le 10\} \]
5. List all the elements of the following sets
(i) A={x:x is an odd natural number}
\[ A = \{1, 3, 5, 7, 9, \ldots\} \](ii) B={x:x∈Z,−1/2
\[ B = \{0, 1, 2, 3, 4\} \](iii) C={x:x∈Z, x²≤4}
\[ C = \{-2, -1, 0, 1, 2\} \](iv) Letters of LOYAL:
\[ D = \{L, O, Y, A\} \](v)Months not having 31 days:
\[ E = \{April, June, September, November, February\} \](vi) Consonants preceding k:
\[ F = \{b, c, d, f, g, h, j\} \]
6. Match the following
- (i) {1, 2, 3, 6} → (c)
- (ii) {2, 3} → (a)
- (iii) {M, A, T, H, E, I, C, S} → (d)
- (iv) {1, 3, 5, 7, 9} → (b)
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