Exercise 1.2 NCERT Class 11 Chapter 1 Sets contains 6 questions. All questions of this exercise have been fully solved. You can access them from the links given below.
Exercise 1.2 NCERT Class 11 contains questions related to the topics such as null sets, types of sets (finite or infinite), and equality of sets.
You can comment and ask for the solution of an exercise if it is not available on the site. Exercise 1.1 has also been solved. Thank you for being here!
Exercise 1.2 NCERT Class 11 Math Solutions
1. Which of the following are examples of the null set.
(i) Set of odd natural numbers divisible by 2
Answer
It is a null set as there is no odd natural number that is divisible by 2.
(ii) Set of even prime numbers
Answer
Set of even prime numbers is not a null set as it is not empty. The set of even prime numbers is given by {2}. 2 is the only even prime number, which is even.
(iii) {}
Answer
The given set {x : x is a natural number, x<5 and x>7} is a null set as there is no natural number which is less than 5 and greater than 7 together.
(iv) { is a point common to any two parallel lines}
Answer
The set of points common to any two parallel lines is a null set as there isn't a point that is common to two parallel lines.
2. Which of the following sets are finite or infinite?
(i) The set of months of a year
Answer
Clearly, the set of months of a year is a finite set containing 12 months.
(ii) {1, 2, 3, . . . }
Answer
The set {1, 2, 3, . . . } is an infinite set as it contains infinite number of natural numbers
(iii) {1, 2, 3, . . . 99, 100}
Answer
The set {1, 2, 3, . . . , 99, 100} is a finite set as it contains a finite number of natural numbers from 1 to 100.
(iv) The set of positive integers greater than 100
Answer
The set of positive integers greater than 100 is an infinite set as there are an infinite number of positive integers greater than 100.
(v) The set of prime numbers less than 99
Answer
The set of prime numbers less than 99 is {2, 3, 5, 7, 11, ..., 97}. This set is clearly a finite set.
3. State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
Answer
The set of lines which are parallel to the x-axis is an infinite set as there can be infinite number of lines that can be drawn parallel to x-axis.
(ii) The set of letters in the English alphabet
Answer
The set of letters in the English alphabet is a finite set , as there are only 26 letters in the English alphabet.
(iii) The set of numbers which are multiple of 5.
Answer
The set of numbers which are multiple of 5 is a finite set , as there can be infinite numbers that are multiples of 5.
(iv) The set of animals living on the earth
Answer
The set of animals living on the earth is a finite set, as we can count the total number of animals on Earth.
(v) The set of circles passing through the origin (0,0)
Answer
The set of circles passing through the origin (0,0) is an infinite set as there can be infinite number of circles which can be drawn passing through the origin (0,0).
4. In the following, state whether A = B or not:
(i)
Answer
A = B , as there are the same and
equal number of elements in A and B.
(ii)
Answer
AB, as 16 ∈ A but 16 ∉ B and 18 ∈ B but 18 ∉ A.
(iii)
Answer
A = B, as all elements of A are positive even integers
and less than 10.
(iv)
Answer
A ≠ B, as A contains multiples of 10
but 15 ∈ B is not a multiple of 10.
5. Are the following pair of sets equal? Give reasons.
(i)
Answer
Let's first find the solution of
We have,
and
Clearly, A ≠ B.
(ii)
Answer
The roster form of the given sets are :
A = {F, O, L, W} and B = {W, O, L, F}
Clearly, A = B
6. 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, },
G = {1, -1},
H = {0, 1}
Answer
From the given sets, the equal sets are as follows:
B = D,
E = G
