# Sets Class- 7th RS Aggarwal Exe-6 B Goyal Brothers ICSE Maths Solution

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 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

= 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

= 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

= 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}

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}

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