Class 6,Maths RS Aggarwal, chapter - Sets

Exercise 7A – Sets

1. Which of the following collections are sets?

1. All persons on earth
2. All male teachers of your school
3. All leaders of India
4. All healthy people of your town
5. All fat boys of your locality
6. All planets in our solar system
7. All difficult problems in your book on Mathematics
8. All 3-digit natural numbers
9. All books in your school library

(ii), (vi), (viii) are sets. Others are not well-defined collections.

2. Describe each set in Roster Form:

1. A = {x : x is a natural number, 5 < x < 14}
2. B = {x : x is a factor of 18}
3. C = {x : x is a prime factor of 330}
4. D = {x : x is a 2-digit number, digits sum to 8}

(i) A = {6, 7, 8, 9, 10, 11, 12, 13}
(ii) B = {1, 2, 3, 6, 9, 18}
(iii) C = {2, 3, 5, 11}
(iv) D = {17, 26, 35, 44, 53, 62, 71, 80, 89}

3. Describe the following sets in Set-Builder Form:

1. A = {16, 18, 20, 22, 24, 26, 28}
2. B = {23, 25, 27, 29, 31, 33, 35}

(i) A = {x : x is an even number, 15 < x < 30}
(ii) B = {x : x is an odd number, 22 < x < 36}

4. Let A = {5, 7, 11, 13, 17, 19, 23, 29}. Insert ∈ or ∉:

1. 7 ___ A
2. 9 ___ A
3. 3 ___ A
4. 15 ___ A

7 ∈ A, 9 ∉ A, 3 ∉ A, 15 ∉ A

5. Let B = {2, 4, 6, ..., 80}. Insert ∈ or ∉:

1. 26 ___ B
2. 31 ___ B
3. 58 ___ B

26 ∈ B, 31 ∉ B, 58 ∈ B

6. True or False:

1. 2 ∈ {x : x is a whole number, x < 10}
2. 2 ∉ {x : x is an integer, 4 < x < 4}
3. 4 ∈ {x : x is an even number, x > 4}

(i) True
(ii) True
(iii) False