NCERT Solutions for Class 11 Maths
Chapter 1- Sets
Exercise 1.2 (Page No- 8 & 9)
Q1 : Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x:x is a natural numbers, x < 5 and x > 7 }
(iv) {y:y is a point common to any two parallel lines}
Answer :
(i) A set of odd natural numbers divisible by 2 is a null set because there is no odd natural number that is divisible by 2.
(ii) A set of even prime numbers is not a null set because 2 is an even prime number.
(iii) {x: x is a natural number, x < 5 and x > 7} is a null set because there cannot be a number simultaneously less than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines} is a null set because parallel lines do not intersect. Hence, a point common to any two parallel lines does not exist.
Q2 :Which of the following sets are finite or infinite
(i) The set of months of a year
(ii) {1, 2, 3 …}
(iii) {1, 2, 3 … 99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less than 99
Answer :
(i) The set of months of a year is a finite set because it has 12 elements i.e
{January, February, March, April, May, June, July, August, September, October, November, December}.
(ii) {1, 2, 3 …} is an infinite set as it is the set of infinite number of natural numbers.
(iii) {1, 2, 3 …99, 100} is a finite set because the numbers from 1 to 100 are finite in number i.e total 100 numbers.
(iv) The set of positive integers greater than 100 is an infinite set because positive integers greater than 100 are infinite.
(v) The set of prime numbers less than 99 is a finite set because prime numbers less than 99 are finite in number.
Q3 : State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)
Answer :
(i) The set of lines which are parallel to the x-axis is an infinite set because there are infinite numbers of lines parallel to the x-axis.
(ii) The set of letters in the English alphabet is a finite set because there are 26 alphabets.
(iii) The set of numbers which are multiple of 5 is an infinite set because there are infinite numbers which are multiples of 5.
(iv) The set of animals living on the earth is a finite set because there are infinite numbers of animals living on the earth.
(v) The set of circles passing through the origin (0, 0) is an infinite set because there are infinite numbers circles which can pass through the origin.
Q4 : In the following, state whether A = B or not:
(i) A = {a, b, c, d}; B = {d, c, b, a}
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10}
(iv) A = {x: x is a multiple of 10}; B= {10, 15, 20, 25, 30 …}
Answer :
(i) A = {a, b, c, d}; B = {d, c, b, a}
The order in which the elements of a set are listed is not significant.
ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18} It can be seen that 12 ∈A but 12 ∉ B and 18 ∈ B but 18 ∉ B
Hence A = B
(iii) A = {2, 4, 6, 8, 10}
B = {x: x is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10}
Hence A = B
(iv) A = {x: x is a multiple of 10} = {10,20,30,40,50,60…}
B = {10, 15, 20, 25, 30 …}
We can see that 15 ∈ B but 15 ∉ A, Similarly 25 ∈ B but 25 ∉ A
Hence A ≠ B
Q5 : Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0}
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
Answer :
(i) A = {2, 3}; B = {x: x is a solution of x2 + 5x + 6 = 0}
We can solve the equation x2 + 5x + 6 = 0 as following:
x(x + 3) + 2(x + 3) = 0 (x + 2)(x + 3) = 0
x = -2 or x = -3
Therefore A = {2, 3}; B = {-2, -3}
Hence A ≠ B
(ii) A = {x: x is a letter in the word FOLLOW} = {F, O, L, W}
B = {y: y is a letter in the word WOLF} = {W, O, L, F}
The order in which the elements of a set are listed is not significant.
Therefore, A = B
Q6 : From the sets given below, select equal sets:
A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}
E = {-1, 1}, F = {0, a}, G = {1, -1}, H = {0, 1}
Answer :
The order in which the elements of a set are listed is not significant.
Hence B = D and E = G