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

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

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

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

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

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}

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}

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.

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

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}

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}

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)

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 :–