Telangana SCERT Class 10 Maths Chapter 2 Sets Exercise 2.1 Maths Problems and Solution Here in this Post. Telangana SCERT Class 10 Maths Solution Chapter 2 Sets Exercise 2.1
Telangana SCERT Solution Class X (10) Maths Chapter 2 Sets Exercise 2.1
Exercise 2.1
(1) Which of the following are sets? Justify your answer
(i) The collection of all the months of a year beginning with the letter “J”
=> Sets:- “The well defend collection of object is called set”
A = {Jan, Jun, Jul}
Therefore, It is a set.
(ii) The collection of ten most talented writers of India.
=> It is not well defined sets because we are not selecting elements of given sets. So, here it is not well defined
Hence it is not a set
(iii) A team of eleven best cricket batsman of the world
=> A = {Sachin, Mahendra …….}
It is not possible to select the best batsman of the world.
So, we are not saying exact elements of sets
Hence, it is not set
(iv) The collection of all boys in your class
=> It has unique elements
Therefore, It is a well defined
Hence it is a set.
(v) The collection of all even integers
=> We can select the unique elements
Therefore, it is well defined.
Hence it is a set.
(2) If A = {0, 2, 4, 6}, B = {3, 5, 7}
And C = {p, q, r}, then fill the appropriate symbol, ∈ or ∉ in the blanks
(i) o —- A { read as ∈ = belongs to }
=> o ∈ A {∉ = dose not belongs to}
O is present in set A
(ii) 3…….C
=> 3 ∈ c
3 is present in set C
(iii) 4 —– B
=> 4 ∈ B
4 is not present in set B
(iv) 8 —- A
=> 8 ∉ A
8 is not present in set A
(v) P………C
=> P ∈ C
P is present in set C
(vi) 7 —- B
=> 7 ∈ B
7 is present in set B
(3) Express the following statements using symbols
(i) The elements ‘x’ does not belong to ‘A’
=> x ∉ A [Because, x is not present in set A]
(ii) ‘d’ is an element of the set ‘B’
=> d ∈ B [d is present in set B]
(iii) ‘1’ belongs to the set of natural numbers
=> 1 ∈ N [Because, Natural numbers = N]
[1 is a natural no]
(iv) ‘8’ does not belong to set of prime numbers P
(vi) 7 —- B
=> 7 ∈ B
7 is present in set B.
(3) Express the following statements using symbol
(i) The elements ‘x’ does not belong to ‘A’
=> x ∉ A [Because, is not present in set A]
(ii) ‘d’ is an element of the set ‘B’
=> d ∈ B [d is preset in set B]
(iii) ‘1’ belongs to the set of natural numbers
=> 1 ∈ N[Because, natural numbers = N]
[1 is a natural no.]
(iv) ‘8’ does not belong to set of prime numbers p
=> 8 ∉ P [Because is not prime number]
(4) State whether the following statements are true or false justify your answer.
(i) 5 ∉ set of prime numbers
=> False.
Since, prime no = {2,3,5,7,……}
So, 5 is a prime number.
(ii) 5 = {5,6,7} implies 8 ∈ 5
=> False.
Since 8 is not in set 5
Therefore, 8 ∉5
(iii) -5 ∉ W where ‘W’ is the set of whole numbers
Answer: True.
Since, whole no = {0, 1, 2, 3, 4, 5….}
Set -5 ∉ W
(iv) 8/11 ∈ Z where ‘Z’ is the set of integers
=> False.
Since, Z = {0, +- 1, +-2, +- 3, +-4 ….}
8/11 is a rational number not a integer
So, 8/11 ∉ Z
(5) Write the following sets in roster form
(i) B = {x : x is a natural number smaller than 6}
=> B = {1, 2, 3, 4, 5} (x , 6)
(ii) C = {x: x is a two digit natural 1 number such that the sum of its digits is 8}
=> C = {17, 71, 26, 35, 44, 53, 62, 80}
{1 + 7 = 8, 7+1 = 8, 2+6 = 8, 3+5 = 8, 4+4 = 8, 5+3 = 8, 6+2 = 8, 8+0 = 8, but 1+2 = 3 so we can’t take 12, 11, 13}
(iii) D = {x: x is a prime number which is a divisor of 60}
=> D = {2, 3, 5}
{divisors of 60 = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}
But we have to take only prime numbers
{1, 4, 6, 10, 12, 15, 20, 30, 60}
are not prime numbers.
(iv) E = {x: x is an alphabet in BETTER}
=> E = { B, E, T, R}
[Because, E is repeat & T is also repeat}
(6) Write the following sets in the set builder form
(1) {3, 6, 9, 12}
=> A = {x : x is a multiple of 3 and x<13}
(ii) {2, 4, 8, 16, 32}
=> C = {x: x = 2n n ∈ N and n ≤ 5}
[Because, 21 = 2, 22 = 4, 23 = 8, 24 = 16, 25 = 32}
(iii) {5, 25, 125, 625}
=> D = {x: x = 5n, n ∈ N and n<5 }
[Because, 51 = 5, 52 = 25, 53 = 125, 54 = 625]
(iv) {1, 4, 9, 16, 25, ……… 1000}
=> E = {x: x = n2, n ∈N and n ≤ 10}
[Because, 12 =1, 22 = 4, 32 = 9, 42 = 16 …..]
(7) Write the following sets in roster form
(i) A = {x: x is a natural number greater than 50 but smaller than 100}
=> A = {51, 25, 53, 54, 55, ….. 98, 99}
[Because, x > 50 and x < 100]
(ii) B = {x: x is an integer, x2 = 4}
=> B = {-2, 2} [Because, 22 = 4 & (-2)2 = 4]
(iii) D = {x : x is a letter in the world “LOYAL”}
=> D = { L, O, y, A}
{Because L is repeat}
{in the set we cannot take a repeated letter}
(IV) E = x : x = 2n2 + 1, -3 ≤ n ≤ 3, n ∈ z}
=> E = {3, 9, 19}
[Because, 2(-1)2 + 1 = 3
2(-2)2 + 1 = 9
2(-3)2 + 1 = 19
(Q8) Match the roster form with set builder form.
(i) {1, 2, 3, 6} [C] a> [x : x is prime number and divisor of 6}
(ii) {2, 3} [a] b> {x : x} is an odd natural no. smaller than 10}
(iii) {m, a, t, h, e, i, c, s} [d] c> {x : x is a natural no. & divisor of 6}
(iv) {1, 3, 5, 7, 9} [b] d> {x : x is a letter of the word MATHEMATICS
Explanations:
(i) x = N = {1, 2, 3, 4, 5, —}
6/2 = 3, 6/3 = 2, 6/6 = 1
4 is not divisor of 6
(ii) x = p = {2, 3, 5, 7, —}
6/2 = 3, 6/3 = 2, 5 is not divisor of 6
(iv) x is an odd natural numbers.
N = {1, 3, 5, 7, —}
x <10
So, we have to take only x <10
{1, 3, 5, —9}