# Sets Class- 7th RS Aggarwal Exe-6 A Goyal Brothers ICSE Maths Solution

Sets Class- 7th RS Aggarwal Exe-6 A Goyal Brothers ICSE Math Solution . We provide step by step Solutions of lesson-6 Sets for ICSE Class-7 Foundation RS Aggarwal Mathematics of Goyal Brothers Prakashan . Our Solutions contain all type Questions of Exe-6 A to develop skill and confidence. Visit official Website for detail information about ICSE Board Class-7 Mathematics in this article we would learn What is set, How to describe a set and type of sets with example.

## Sets Class- 7th RS Aggarwal Exe-6 A Goyal Brothers ICSE Maths Solution

 Board ICSE Publications Goyal brothers Prakashan Subject Maths Class 7th Chapter-6 Sets Writer RS Aggrawal Book Name Foundation Topics Solution of Exe-6 A Academic Session 2023 – 2024

### What isSets?

What are the 3 ways of describing a set? How do you describe the elements of a set?How do you verbally describe a set? describing sets examples

### How to Describe a Set?

I. Roster Method or Tabular Form

II. Description Method

III. Rule Method or Set-Builder Form

### Types of Sets

1. Finite set

2. Infinite set

3. Empty set or Null set

4. Singleton set

5. Equal sets

6. Cardinal number of a set

7. Equivalent sets

8. Disjoint sets

9. Overlapping sets

### Exercise – 6 A

Sets Class- 7th RS Aggarwal Goyal Brothers ICSE Maths Solution

#### 2. Write each of the following sets in Roster form :

##### (i) A = set of all prime numbers between 70 and 100.

Answer:  A = {71, 73, 79, 83, 89, 97}

##### (ii) B = set of all whole numbers less than 8.

Answer: B = {0, 1, 2, 3, 5, 6,7}

##### (iii) C = set of all integers lying between -7 and 2.

Answer:  C = {-6, -5, -4, -3, -2, -1, 0, 1}

##### (iv) D = set of all composite numbers between 23 and 33.

Answer:  D = {24, 25, 26, 27, 28, 30, 32}

##### (v) E = set of all letters in the word, ‘MATHEMATICS’.

Answer:  E = {M, A, T, H, E, I, C, S}

##### (vi) F = set of all consonants in the word, ‘SECONDARY’.

Answer:  F = {S, C, N, D, R, Y}

##### (vii) G = set of vowels in the word, ‘INTERMEDIATE’.

Answer:  G = {I, E, A}

#### 3. Write each of the following sets in Roster form and write the cardinal number of each :

##### (i) A = {x : x is an integer, -3 < x ≤ 4}.

Answer:  A = {-2, -1, 0, 1, 2, 3, 4}, n(A) = 7

##### (ii) B = {x : x ∈ N, 3x – 6 < 9}.

Answer: B = {1, 2, 3, 4}, n(B) = 4

##### (iii) C = {x : x = n2 , n ∈ N, 10 < n < 16}.

Answer:  C = {121, 144, 169, 196, 225}, n(C) = 5

##### (iv) D = {x : x ∈ W, x – 3 < 2}.

Answer: D = {0, 1, 2, 3, 4}, n(D) = 5

##### (v) E = {x : x = 2n – 1, n ∈ N and n < 6}.

Answer:  E = {1, 3, 5, 7, 9}, n(E) = 5

##### (vi) F = {x : x is a letter in the word ‘COMMON’}.

Answer: F = {C, O, M, N}, n(F) = 4

##### (vii) G = {x : x is a primary colour}.

Answer: G = {Red, Blue, Yellow}, n(G) = 3

##### (viii) H = {x : x is a digit in the numeral 2362}.

Answer: H = {2, 3, 6}, n(H) = 3

##### (ix) J = {x : x = (1/n), n ∈ N, 4 < n < 10}.

Answer:  J = {(1/5), (1/6), (1/7), (1/8), (1/9)}, n(J) = 5

#### 4. Write each of the following sets in set-builder form :

##### (i) A = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18}.

Answer: A = {x : x is a composite number, 1 < x < 20}

##### (ii) B = {1, 2, 3, 5, 6, 10, 15, 30}.

Answer: B = {x : x is a factor of 30}

##### (iii) C = {-9, -6, -3, 0, 3, 6, 9, 12, 15}.

Answer: C = {x : x = 3n, n ∈ I, -3 ≤ n ≤ 5}

##### (iv) D = {(1/2), (2/3), (3/4), …., (8/9)}.

Answer:  D = {x : x = n/(n+1), n ∈ N, 1 ≤ n ≤ 8}

##### (v) E = {(1/3), (1/5), (1/7), (1/11), (1/13), (1/17), (1/19)}.

Answer:  E = {x : x = (1/n), n is prime, 2 < n < 20}

##### (vi) F = {April, June, September, November}.

Answer:  F = {x : x is a month of a year having 30 days}

##### (vii) G = {0}.

Answer:  G = {x : x + 1 = 1, x ∈ W}

##### (viii) H = { }.

Answer:  H = {x : x is a number, x ≠ x}

#### 6. Identify the null sets among the following :

##### (i) A = {x : x is a whole number, x < 1}.

Answer:  A = {0} Which is not a null set…..

##### (ii) B = {x : x is a number, x > x}.

Answer:  B = { } Which is a null set…..

##### (iii) C = {x : x is an even prime number}.

Answer:  C = {2} Which is not a null set…..

##### (iv) D = {x : x ∈ I, x2 = -4}.

Answer:  D = { } Which is a null set…..

##### (v) E = {x : x is a perfect square number, 40 < x < 50}.

Answer:  E = {49} Which is not a null set…..

##### (vi) F = {x : x ∈ N, 5 < x < 6}.

Answer:  F = { } Which is a null set…..

#### 7. Identify whether the given pair consists of equal or equivalent but not equal sets or none :

##### B = set of letters of the word ‘FOLLOWER’.

Answer:  A = (F, L, O, W, E, R)….

B = (F, O, L, W, E, R)….

(A=B) Which is equal set….

##### (ii) C = {x : x ∈ N, x + 5 = 6} and D = {x : x ∈ W, x < 1}.

Answer:  C = (x : x + 5 = 6)

= (x : x = 6 – 5)

= (x : x = 1)

C = (1)….

D = (x : x ∈ W, x < 1)

= {0} (C↔D) Which is equivalent but not equal.

##### (iii) E = set of first five whole numbers.

F = set of first five natural numbers.

Answer: E = (0, 1, 2, 3, 4)

F = (1, 2, 3, 4, 5)

(E↔F)Which is equivalent but not equal.

##### (iv) G = {a, b, c} and H = {x, y, z}.

Answer:  G = (a, b, c)….

H = (x, y, z)

(G↔H)Which is equivalent but not equal.

##### (v) J = {x : x ∈ N, x ≠ x} and K = {x : x ∈ N, 6 < x < 7}.

K = { }

(J = K)Which is equal.

#### 8. For each of the following pairs of sets, identify the disjoint and overlapping sets :

##### B = {x : x is an even natural number, x < 8}.

Answer:  A = 2, 3, 5, 7

B = 2, 4, 6

Which are the overlapping sets…..

##### (ii) C = {x : x ∈ N, x < 10} and D = {x : x ∈ N, x is a multiple of 5}.

Answer:  C = 1, 2, 3, 4, 5, 6, 7, 8, 9

D = 5, 10, 15, 20, 25

Which are the overlapping sets…..

##### (iii) E = {x : x = 4n, n ∈ N} and F = {x : x = 9n, n ∈ N}

[Hint : 36 ∈ E and 36 ∈ F.]

Answer: E = 4, 8, 12, 16, 20, 24, 28, 32, 36

F = 9, 18, 27, 36

Which are the overlapping sets…..

##### (iv) G = {x : x = 8n, n ∈ N and n < 7} and H = {x : x = 9n, n ∈ N and n < 7}.

Answer:  G = 8, 16, 24, 32, 40, 48

H = 9, 18, 27, 36, 45, 54

∴ These set has no common element

∴ These are disjoint sets

#### 9. State in each case, whether the given statement is true or false :

 Statement True/False (i) If A is the set of all non-negative integers, then 0 ∈ A. T (ii) If B is the set of all consonants, then c ∈ B. T (iii) If C is the set of all prime numbers less than 80, then 57 ∈ C. F (iv) {x : x ∈ W, x + 5 = 5} is a singleton set. T (v) If D = {x : x ∈ W, x < 4}, then n(D) = 4. T (vi) {a, b, c, 1, 2, 3} is not a set. F (vii) {1, 2, 3, 1, 2, 3, 1, 2, 3, ……} is an infinite set. F (viii) 0 ∈ ∮. F (ix) {3, 5} ∈ {1, 3, 5, 7, 9}. F

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