**Sets** Class- 7th RS Aggarwal Exe-6 B 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 B to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-7 Mathematics. in this article we would learn Subset and superset, proper subset, number of all possible subsets of a given set, universal set, complement of a set. What is subset and superset with example? What is the difference between ⊆ and ⊂?What is called superset? What is called subset?

## Sets Class- 7th RS Aggarwal Exe-6 B 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 B |

Academic Session | 2023 – 2024 |

**What is subset and superset with example?**

If A is a subset of B, then A is contained in B. It implies that B contains A, or in other words, B is a superset of A. We write A ⊇ B to denote that B is a superset of A. For example, if A = {1, 3} and B = {1, 2, 3}, Since all the elements in A contained in B so B is a superset of A because B contains A.

**What is the difference between ⊆ and ⊂?**

A⊆B A ⊆ B asserts that A is a subset of B : every element of A is also an element of B. B . A⊂B A ⊂ B asserts that A is a proper subset of B : every element of A is also an element of B, but A≠B.

**What is called superset?**

A superset in math can be defined as a set of elements containing all of the elements of another set. In other words, A is a superset of B if it contains all of the elements of B. For example, consider the following two sets: Set A elements are {1,2,3,4,5,6,7,8,9,10} Set B elements are {1,3,5,7,,9}

**What is called subset?**

A set A is a subset of another set B if all elements of the set A are elements of the set B. In other words, the set A is contained inside the set B. The subset relationship is denoted as A⊂B.

**Exercise – 6 B**

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

**1. Indicate whether the given statement is true or false :**

Statement |
True/False |

(i) {Triangles} ⊆ {Quadrilaterals} | F |

(ii) {Squares} ⊆ {Rectangles} | T |

(iii) {Rhombuses} ⊆ {Parallelograms} | T |

(iv) {Natural numbers} ⊆ {Whole numbers} | T |

(v) {Integers} ⊆ {Whole numbers} | F |

(vi) {Composite numbers} ⊆ {Odd numbers} | F |

**2. Write down all possible subsets of each of the sets given below :**

**(i) {1}**

**Answer:** Subsets of {1} are ∅, {1}

**(ii) {3, 4}**

**Answer:** Subsets of {3, 4} are ∅, {3}, {4}, {3, 4}

**(iii) {2, 3, 5}**

**Answer:** Subsets of {2, 3, 5} are ∅, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}

**(iv) ∅**

**Answer:** Subsets of ∅ is ∅

**(v) {c, d, e}**

**Answer:** Subsets of {c, d, e} are ∅, {c}, {d}, {e}, {c, d}, {c, e}, {d, e}, {c, d, e}

**(vi) {a, b, c, d}**

**Answer:** Subsets of {a, b, c, d} are ∅, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d}

**3. Write down all possible proper subsets of each of the sets given below :**

**(i) {x}**

**Answer:** Proper subset of ‘x’ is ∅

**(ii) {p, q}**

**Answer:** Proper subset of (p, q) are ∅, (p), (q)

**(iii) {m, n, p}**

**Answer:** Proper subset of (m, n, p) are ∅, (m), (n), (p), (m, n), (m, p), (n, p)

**(iv) {1, 2, 3, 4}**

**Answer:** Proper subset of (1, 2, 3, 4) are ∅, (1), (2), (3), (4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (1, 2, 3), (1, 3, 4), (2, 3, 4), and (1, 2, 4)

**4. Write down :**

**(i) The set C of letters of the word ‘PAPAYA’.**

**Answer:** C = P, A, Y

**(ii) All subsets of C.**

**Answer:** ∅, (P), (A), (Y), (P, A), (P, Y), (A, Y), (P, A, Y)

**(iii) All proper subsets of C.**

**Answer:** ∅, (P), (A), (Y), (P, A), (P, Y), (A, Y)

**5. How many subsets in all are there of a set containing 4 elements ?**

**Answer: **Number of element (n) = 4

Number of subset = 2^{n}

**= **2^{4}

**= **2 × 2 × 2 × 2

**= **16

**6. How many subsets in all are there of a set with cardinal number 6 ?**

**Answer: **Number of element (n) = 6

Number of subset = 2^{n}

= 2^{6}

= 2 × 2 × 2 × 2 × 2 × 2

= 64

**7. How many proper subsets in all are there of a set containing 3 elements?**

**Answer: **Number of element (n) = 3

Number of proper subset = 2^{n}-1

#### = 2^{3}-1

#### = 2 × 2 × 2 – 1

= 8 – 1

= 7

**8. How many proper subsets in all are there of a set with cardinal number 5 ?**

**Answer: **Number of element (n) = 5

Number of proper subset = 2^{n}-1

#### = 2^{5}-1

#### = 2 × 2 × 2 × 2 × 2 – 1

= 32 – 1

= 31

**9. Write of the following statements are true ?**

Statement |
True/False |

(i) {a} ⊂ {a, b, c} | T |

(ii) {a} ⊂ {b, c, d, e} | T |

(iii) ∅ ⊂ {a, b, c} | F |

(iv) ∅ ∈ {a, b, c} | T |

(v) 0 ∉ ∅ | T |

(vi) {1} ⊂ {0, 1} | F |

(vii) Every subset of a finite set is finite. | F |

(viii) Every subset of an infinite set is infinite. | F |

**10. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Write the subset of A containing :**

**(i) all odd numbers**

**Answer:** all odd numbers = {1, 3, 5, 7, 9, 11}

**(ii) all prime numbers**

**Answer:** all prime numbers = {2, 3, 5, 7, 11}

**(iii) all multiples of 4**

**Answer:** all multiples of 4 = {4, 8, 12}

**11. Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} be the universal set and let A = {5, 7, 11, 13}, B = {6, 8, 10, 12, 14, 16} and C = {5, 6, 8, 10, 11, 12} be its subsets :**

**Find : (i) A′ **

**Answer:** A′ = U – A = {6, 8, 10, 12, 14, 15, 16,}

**(ii) B′ **

**Answer:** B′ = U – B = {5, 7, 9, 11, 13, 15}

**(iii) C′ **

**Answer:** C′ = U – C = {7, 9, 13, 14, 15, 16}

**12. Let the set I of all integers be the universal set and let A = {x : x is a negative integer} be its subset. Find A′.**

**Answer: **§ = {set of all integers}

= {… -3, -2, -1, 0, 1, 2, 3,…..}

A = {x/x is a negative integer}

= {… -3, -2, -1}

A′ = set of those elements of § which are not is A = {0, 1, 2, 3…} = set of W

A′ = {x /x is a whole}

**13. Suggest a universal set for the sets given below :**

**(i) {5, 7, 9}, {3, 5, 7}, {1, 3, 9} and {2, 4, 8}**

**Answer: **Universal set

U = 1, 2, 3, 4, 5, 6, 7, 8, 9

**(ii) {odd numbers less than 8}, {prime numbers less than 8} and {even numbers between 3 and 8}.**

**Answer: **(odd numbers less than 8 are 1, 3, 5, 7), (prime numbers less than 8 are 2, 3, 5, 7) and (even numbers between 3 and 8 is 4, 6) U = 1, 2, 3, 5, 6, 7

**(iii) {vowels in English alphabet}, {consonants in English alphabet}.**

**Answer: **Universal set of the given sets will be

§ {x : x is a letter in English Alphabet}

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

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