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 = 2n
= 24
= 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 = 2n
= 26
= 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 = 2n-1
= 23-1
= 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 = 2n-1
= 25-1
= 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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