**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 **CISCE** 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 is** **Sets?**

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

**1. Which of the following collections are sets ?**

**(i) All books in your school library.**

**Answer:** Yes

**(ii) All red flowers in a park.**

**Answer:** Yes

**(iii) All good players in your school.**

**Answer:** No

**(iv) All fiction movies.**

**Answer:** Yes

**(v) All easy problems in your book on mathematics.**

**Answer:** No

**(vi) All poor people in Mumbai.**

**Answer:** No

**(vii) All boys in your class weighing less than 50 kg.**

**Answer:** Yes

**(viii) All persons of repute in your colony.**

**Answer:** No

**(ix) All even numbers greater than 100.**

**Answer:** Yes

**(x) All integers less than -5.**

**Answer:** Yes

**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 = n**^{2} , n ∈ N, 10 < n < 16}.

^{2}, 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}

**5. State whether the given set is finite or infinite :**

**(i) Set of all even natural numbers.**

**Answer:** Infinite

**(ii) Set of all odd integers.**

**Answer:** Infinite

**(iii) Set of all rivers in India.**

**Answer:** Finite

**(iv) Set of all points on a line segment 1 cm long.**

**Answer:** Infinite

**(v) Set of all factors of 1200.**

**Answer:** Finite

**(vi) Set of all multiples of 6.**

**Answer:** Infinite

**(vii) Set of all drops of water in a bucket.**

**Answer:** Infinite

**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, x^{2} = -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 :**

**(i) A = set of letters of the word ‘FLOWER’.**

**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}.**

**Answer:** J = { }

K = { }

(J = K)Which is equal.

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

**(i) A = {x : x is a prime number, x < 8}.**

**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 |

**— : end of Sets Class- 7th RS Aggarwal Exe-6 A Goyal Brothers ICSE Maths Solution:–**

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