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**Number Line Prime Class 7 Solutions Chapter 1 Sets**

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Number Line Prime Class 7 Math Book, Chapter 1, Sets. Here students can easily find step by step solutions of all the problems for Sets, Exercise 1A, 1B and 1C Also here our Mathematics Teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here on this post students will get chapter 1 solutions. Here in this post all the solutions are based on latest Syllabus.

**Sets Exercise 1A all question Solutions :**

**Question no – (1)**

**Solution : **

**(a) all the tall students in your school**

= Not a well defined set.

**(b) all the commerce students in your school**

= It is a well defined set.

**(c) all the rich industrialists in your country**

= Not a well defined set.

**(d) all the even numbers greater than 7 but less than 23**

= It is a well defined set.

**(e) collection of odd natural number less than 20**

= It is a well defined set.

(**f) collection of medicinal plants in your country**

= Not a well defined set

**(g) collection of medicinal plants in your country**

= It is a well defined set

**(h) collection of all public schools in your city**

= It is a well defined set.

**Question no – (2) **

**Solution : **

**Let O = {1,3,5,7,9},**

**E = {2,4,6,8,10}**

**(a) 1__E**

= 1 ∉ E

**(b) 2__ O**:

= 2 ∉ O

**(c)1 __ O**:

= 1 ∉ O

(**d) 4__ E**:

= 4 ∉ E

**(e) 0.1__O**

= 0.1 ∉ O

**(f) 10__E**

= 10 ∉ E

**Question no – (3) **

**Solution : **

**(a) O = {x : x =2n +1, n ****∉**** N}**

= O = { x : x = 2 n = 1 ;n ∉ N}

= { odd natural numbers greater than one }

**(b) E = {x : x = 2n**^{2 }**, n ****∉**** N}**

= E = { x : x = 2n^{2 }, n ∉ N }

= { Twice the square of natural numbers}

**Question no – (4)**

**Solution :**

**(a) set of the whole numbers that are less than 10**

= A = { 0,1,2,3,4,5,6,7,8,9}

**(b) set of the consonants in the English alphabet**

= C = { b, c, d, f, g, h, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z,}

**(c) set of two-digit numbers, the sum of whose digits is 8**

= S = { 17, 26, 35, 44, 53, 62, 71, 81}

**(d) squares of all the natural numbers less than 13**

= D = { 1, 2, 3, }

**(e) {x | x is a letter in the word TUMBLER}**

= L = { T, U, M, B, L, E, R }

(**f) { x | x is a vowel in the word ROCKET}**

= v = {O , E**}**

**(g) set of all the months in a year that have only 30 days**

= M = {April, June, September, November}

**(h) set of all the months in the year that have at least 30 days**:

= h = { January, March, April, May June, July, August, September, October, November, December}

**Question no – (5)**

**Solution :**

**(a) A = {1, 4, 9, 16, 25, 36, 49,64}**

= A = {1, 4, 9, 16, 25, 36, 49,64}

= {x : x = n^{2}, o<n ,9, n ∉ N}

**(b) B = {0, 3, 8, 15, 24, 35, 48, 63}**

= B = {0, 3, 8, 15, 24, 35, 48, 63}

**(c)** {x : x = n^{2}-1 , n ∉ N , n<9}

= C = set of multiples of 9

= { x : x = 9n, n ∉ N}

**(d) set of multiples of 5**

= D = set of multiples of 5

={ x : x = 5n , n ∉ N}

**(e) set of vowels in the word ENCYCLOPEDIA**

= V = set of vowels in the word ENCYCLOPEDIA

= { x : x is a vowels in the word Encyclopedia}

**Sets Exercise 1B all question Solutions :**

**Question no – (1)**

**Solution :**

**(a) Set of four consecutive natural numbers**

= finite

**(b) Set of odd number****:**

= finite

(**c) Set of multiples of 8 greater than 7 and less than 80**

= Finite

**(d) Set of the letters of the word THEORETICAL**

= Infinite

**(e) Set of the number of the UNO**

= Infinite

**(f) Set of the multiples of 3**

= Infinite

**Question no – (2)**

**Solution :**

**(a) Set of the vowels in the w3ord DANGEROUS**

= Non – empty

**(b) Set of the multiples of 5 more than 6 and less than 11**

= Singleton

**(c) A = {x : x ****∉****N and x +4 = 7}**

= Singleton

**(d) A = { x : x ****∉**** N and 3x+4 =9}**

= Empty

**(e) Set of the multiples of 6 greater than 5 and less than 12**

= Singleton

**(f) Set of the multiples of 3 greater than 2 and less than 7**

= Non – empty

**Question no – (3)**

**Solution : **

**(a) A = {2, 4, 8, 16, 32}**

A = {2, 4, 8, 16, 32}

The number of elements in set A is 5.

There fore the cardinal number of set A is 5.

**∴** n(a) =5

(**b) B = {1, 8, 27, 64, 125}**

B = {1, 8, 27, 64, 125}

**∴** n(B) = 5

**(c) c = {x| x ****∉**** z , -3 ≤ x ≤5}**

c = {x| x ∉ z , -3 ≤ x ≤5}

= {x -3,-2, -1, 0, 1, 2, 3, 4, 5}

**∴** n (c)= 9

**(d) D = {0, 1, 3}**

D = {0, 1, 3}

∴ n(D) = 3

**(e) E = {x | x = 2n +1, 1≤ n ≤ 5 and n ****∈**** N}**

E = {x | x = 2n +1, 1≤ n ≤ 5 and n ∈ N}

= {3, 5, 7, 9, 11}

**∴** n(E) = 5

**(f) F = {x | x ****∈**** N, x = 3z**^{2 }**– 1, -1 ≤ z 2 and z ****∈**** |}**

F = {x | x ∈ N, x = 3z^{2 }– 1, -1 ≤ z 2 and z ∈ |}

= {2, 11}

**∴** N (F) = 2

**Question no – (4) **

**Solution : **

**(a) A ={x 1 | x= 2n – 1, 1** **≤ n 6, n** **∈****N}, B = {x | x = 2n, 1 ≤ n ≤ 6, n ****∈**** N}**

A ={x 1 | x= 2n – 1, 1 ≤ n 6, n ∈N},

B = {x | x = 2n, 1 ≤ n ≤ 6, n ∈ N}

A = {1, 3, 5, 7, 9, 11}

B = {2, 4, 6, 8, 10, 12}

**∴** n(A) = 6 and n (B) = 6

**∴** A equivalent to B

**(b) A = set of vowels in the word MORAL, B = set of vowels in the word ARTISTIC**

A = set of vowels in the word MORAL,

B = set of vowels in the word ARTISTIC

A = {O , A}, B = {A, I, I}

**∴** n(A)=2 and n(B)= 3

**∴ **A is non-equivalent to B

**(c) A = {a, c, e, g}, B = {1, 3, 5, 7, 9}**

A = {a, c, e, g}, B = {1, 3, 5, 7, 9}

**∴** n(A) = 4 and n(B) = 5

**∴** A is non-equivalent to B

**(d) A = {x | x ****∈**** N, x is prime ad 1** **≤ x ≤ 6}, B ={x | x ****∈**** N, x is composite and 1 ≤ x ≤ 8}**

A = {x | x ∈ N, x is prime ad 1 ≤ x ≤ 6},

B ={x | x ∈ N, x is composite and 1 ≤ x ≤ 8}

A = {2, 3, 5}, B ={4, 6, 8}

**∴** n(A) = 3 and n(B)= 3

**∴** A equivalent to B

**(e) A = set of multiples of 9 more than 16, less than 50, B = set of multiples of 3 more than 17 and less than 35,**

A = set of multiples of 9 more than 16, less than 50,

B = set of multiples of 3 more than 17 and less than 35,

A = {18, 27, 36, 45}, B ={ 18, 21, 24, 27, 30, 33,}

**∴** n(A) = 4 and n(B) = C

**∴ **A is non-equivalent to B

**(f) A = set of multiples of 5 less than 30, B ={5, 10, 15, 20, 25}**

A = set of multiples of 5 less than 30,

B = {5, 10, 15, 20, 25}

A = {5, 10, 15, 20, 25}

**∴** As a and B have the same elements, they are equal .

**Sets Exercise 1C all question Solutions :**

**Question no – (1)**

**Solution : **

**(a) {Triangle} ****⊆**** {Polygon}**

= True

**(b) {Square} ****⊆**** {Rhombus}**

= True

**(c) {Parallelogram} ****⊆**** {Trapezium}**

= False

**Question no – (2)**

**Solution :**

A = {0, 2, 4, 6, 8, 10}, B = {6, 10, 12),

C = {0, 2, 4, 8}, D = {8, 12, 10},

**(a) C ****⊂**** A**

Given statement is True

**(b) B** **⊂**** D**

Given statement is False

**(c) C ****⊂**** D**

Given statement is False

**(d) D ****⊂**** B**

Given statement is False

**(e) D ****⊂**** A**

Given statement is False

**Question no – (3) **

**(a) {3}**

Φ = {3}

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

Φ, {p}, {q}, {p, q},

**(c) {2, 5, 7}**

Φ, {2}, {5}, {7}, {2, 5},{2,7},{5,7},{2,5,7}

**(d) Φ**

D = Φ , Φ

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

{1, 2, 3, 4}

Φ, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4},{2,2}, {2,4}, {3,4}, {1,2,3,}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4}

**Question no – (4) **

**Solution : **

**(a) A = {a},**

= A = {a}

= Φ

**(b) {1, 2, 3}**

= B = {1,2,3}

= Φ, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}

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

= {a, b, c}

= Φ, {a}, {b}, {c}, {a, b}, {b, c}, {c, a,}

(**d) { l, m, n, o }**

= { l, m, n, o }

= Φ, {l}, {m}, {n}, {o}, {l, m}, {l, n}, {l, o}, {m, n}, {m, o}, {n, o}, {l, m, n}, {l, m, o}, {l, n, o}, {m, n, o}

**(e) {4, 6, 8, 9}**

= {4, 6, 8, 9}

= Φ, {4},{6},{8}, {9},{4, 6}, {4, 8},{4, 9}, {6, 8}, {6, 9}, {8, 9}, { 4, 6, 8}, {4, 6, 9} ,{6, 8, 9}, {4,8,9}

**Question no – (5) **

**Solution**:

U = {1, 2, 3, 4, 5 6, 7, 8, 9, 10, 11, 12, 13, 14},

**(a) All even numbers**

= E = {2, 4, 6, 8, 10, 12, 14}

**(b) All prime numbers**

= P = {2, 3, 5, 7, 11, 13}

**(c) All composite number**

= C = {4, 6, 8, 9, 10, 12, 14}

**(d) All multiples of 3**

= M = {3, 6, 9, 12}

**(e) All odd prime number**

= O = {3, 5, 7, 11, 13}

**(f) All even prime numbers**

= E = {2}

**Question no – (6) **

**Solution : **

**(a) {a, b, c}, {d, e, f}, {a, e}, {b, c, d}**

= U = {a, b, c, d, e, f}

**(b) {odd numbers less than 9}, {prime numbers less than 5}, {even numbers greater than 2 but less than 9}**

= A = {1, 3, 5, 7}, b = { 2, 3,}

= C = {4, 6, 8}

**∴** u = {1, 2, 3, 4, 5, 6, 7, 8}

**Next Chapter Solution : **