Sets Class 8 RS Aggarwal Exe-5B Goyal Brothers ICSE Maths Solutions Ch-5. We provide step by step Solutions of council prescribe textbook / publication to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

## Sets Class 8 RS Aggarwal Exe-5B Goyal Brothers ICSE Maths Solutions

Board | ICSE |

Publications | Goyal Brothers Prakshan |

Subject | Maths |

Class | 8th |

writer | RS Aggarwal |

Book Name | Foundation |

Ch-5 | Set |

Exe-5B | Subsets |

Edition | 2024-2025 |

### Subsets, Proper Subset, Power Set, Universal Set

**Page- 74, 75**

**Exercise- 5B**

**Que-1: Write down the following statements, using set notation :**

(i) Set A is a proper subset of set B (ii) Set C is a superset of set D. **(iii) Set B contains set A (iv) Neither A is a subset of B, nor B is a subset of A**

(i) Set A is a proper subset of set B (ii) Set C is a superset of set D.

**Solution- **(i) A ⊂ B (ii) C ⊇ D (iii) B ⊇ A (iv) A ⊄ B** **and B ⊄ A

**Que-2: Let A = {all quadrilaterals}, B = {all rectangles}, C = {all squares} and D = {all rhombuses} in a plane. State, giving reasons, whether the following statements are true and false :**

(i) B ⊂ C ⊂ A (ii) C ⊂ B ⊂ A (iii) C ⊂ D ⊂ A (iv) D ⊂ C ⊂ A (v) A ⊇ B ⊇ C (vi) A ⊆ B ⊆ C

(i) B ⊂ C ⊂ A (ii) C ⊂ B ⊂ A (iii) C ⊂ D ⊂ A (iv) D ⊂ C ⊂ A (v) A ⊇ B ⊇ C (vi) A ⊆ B ⊆ C

**Solution- **(i) False (ii) True (iii) True (iv) False (v) True (vi) False

**Que-3:**** Let A = {all triangles}, B = {all isosceles triangles} and C = {all equilateral triangles}. State, giving reasons, whether the following statements are true and false :**

(i) B ⊂ C ⊂ A (ii) C** ⊂ B ⊂ A**

(i) B ⊂ C ⊂ A (ii) C

**Solution- **(i) False (ii) True

**Que-4: Let A = {1,2}. State which of the following statements are true :**

(i) 1 ⊂ A (ii) {1} ∈ A (iii) 1 ∈ A (iv) ø ∈ A (v) ø ⊂ A (vi) {1} ∉ A

(i) 1 ⊂ A (ii) {1} ∈ A (iii) 1 ∈ A (iv) ø ∈ A (v) ø ⊂ A (vi) {1} ∉ A

**Solution- **(i) False (ii) False (iii) True (iv) False (v) True (vi) False

**Que-5: Which of the following statements are correct ?**

(i) a ⊂ {a,b,c} (ii) {a} ∈ {a,b,c} (iii) {a} ⊂ {a,b,c} (iv) ø ∈ {a,b,c} (v) ø ⊂ {a,b,c} (vi) {ø} ⊂ {a,b,c} (vii) a ∈ {{a},b} (viii) {a} ⊆ {{a},b} (ix) {a,b} ∈ {{a,b},c}

(i) a ⊂ {a,b,c} (ii) {a} ∈ {a,b,c} (iii) {a} ⊂ {a,b,c} (iv) ø ∈ {a,b,c} (v) ø ⊂ {a,b,c} (vi) {ø} ⊂ {a,b,c} (vii) a ∈ {{a},b} (viii) {a} ⊆ {{a},b} (ix) {a,b} ∈ {{a,b},c}

**Solution- **(i) False, ‘a’ is not a subset.

(ii) False, {a} is not a element of {a,b,c}

(iii) True, {a} is a subset.

(iv) False, ø is not a element.

(v) True, ø is a subset.

(vi) False, {ø} is not a subset.

(vii) False, ‘a’ is not a element of {{a},b}

(viii) False, {a} is not a subset.

(ix) True, {a,b} is an elements of a set.

**Que-6: Which of the following statements are true ?**

(i) ø = {0} (ii) ø = {ø} (iii) ø ∈ {0} (iv) ø ∈ {ø} (v) ø ∈ {ø,{0}} (vi) {ø} ⊂ {0}

(i) ø = {0} (ii) ø = {ø} (iii) ø ∈ {0} (iv) ø ∈ {ø} (v) ø ∈ {ø,{0}} (vi) {ø} ⊂ {0}

**Solution- **(i) False, ø is an empty set and ø is a set having one element which ø.

(ii) False, ø is an empty set and ø is a set having one element which ø.

(iii) False, ø is an empty set and ø is a set having one element which ø.

(iv) True, ø belongs to the set ø

(v) True, ø belongs to the set ø

(vi) False, ø is an empty set and ø is a set having one element which ø.

**Que-7: Which of the following statements are true ?**

(i) For any two sets A and B, either A ⊆ B or B ⊆ A

(ii) Every subset of a finite set is finite.

(iii) Every subset of an infinite set is infinite.

(iv) Every set has a proper subset

(v) If A has n elements, then P(A) has 2^n subsets.

(i) For any two sets A and B, either A ⊆ B or B ⊆ A

(ii) Every subset of a finite set is finite.

(iii) Every subset of an infinite set is infinite.

(iv) Every set has a proper subset

(v) If A has n elements, then P(A) has 2^n subsets.

**Solution- **(i) False (ii) True (iii) False (iv) False (v) True

**Que-8: Let A be the set of letters in the word, ‘seed’. Find :**

(i) A (ii) n(A) (iii) number if subsets of A (iv) number of proper subsets of A

(i) A (ii) n(A) (iii) number if subsets of A (iv) number of proper subsets of A

**Solution- **(i) A = {s,e,d} (ii) n(A) = 3 (iii) 8 (iv) 7

**Que-9: Find all possible subsets of each of the following sets :**

(i) A = {4,9} (ii) B = {2,3,8} (iii) C = {0,1,2}

(i) A = {4,9} (ii) B = {2,3,8} (iii) C = {0,1,2}

**Solution- **(i) A = ø,{4},{9},{4,9}

(ii) B = ø,{2},{3},{8},{2,3},{3,8},{2,8},{2,3,8}

(iii) C = ø,{0},{1},{2},{0,1},{1,2},{0,2},{0,1,2}

**Que-10: Find the power set of each of the following sets :**

(i) A = {0,5} (ii) B = {7,9} (iii) C = {2,4,6}

(i) A = {0,5} (ii) B = {7,9} (iii) C = {2,4,6}

**Solution- **(i) P(A) = {ø,{0},{5},{0,5}}

(ii) P(B) = {ø,{7},{9},{7,9}}

(iii) P(C) = {ø,{2},{4},{6},{2,4},{4,6},{2,6},{2,4,6}}

**Que-11: Let A = {1,2}. Find the power set of A.**

**Solution- **P(A) = {ø,{1},{2},{1,2}}

**Que-12: Let U = {x: x∈N, x<50}, A = {x: x²∈U}, B = {x: x=n², n∈N} and C = {x: x is a factor of 36}. List the elements of each of the sets A,B and C. Also, state whether each of the following statements is true or false :**

(i) A⊆B (ii) A=B (iii) A↔B (iv) B↔C (v) n(A) < n(C)

(i) A⊆B (ii) A=B (iii) A↔B (iv) B↔C (v) n(A) < n(C)

**Solution- **U = {1,2,3,4,5,6,……….,50}

A = {1,2,3,4,5,6,7}

B = {1,4,9,16,25,36,49}

C = {1,2,3,4,6,9,12,18,36}

(i) False

(ii) False

(iii) True

(iv) False

(v) True

— : End of Sets Class 8 RS Aggarwal Exe-5B Goyal Brothers ICSE Maths Solutions of questions :–

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