Sets Exercise 1.2 NCERT Solutions Class 11 Maths focuses on understanding different types of sets and their properties. This exercise helps students identify finite and infinite sets, equal and equivalent sets, and singleton and empty sets. It builds a strong conceptual base for advanced topics in set theory and is important for CBSE exams as well as competitive exams like JEE, NDA, IMUCET, and Merchant Navy entrance tests.
Chapter 1 SETS Exercise 1.2 NCERT Solutions for Class 11 Maths
NCERT Question 1 : 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}
Solution :
(i) Set of odd natural numbers divisible by 2
Yes, this is a null set because there is no odd natural number divisible by 2.
(ii) Set of even prime numbers
No, this is not a null set because $2$ is an even number which is prime.
(iii) ${x : x \text{ is a natural number},\ x < 5 \text{ and } x > 7}$
Yes, this is a null set because there is no natural number less than $5$ and greater than $7$.
(iv) ${y : y \text{ is a point common to any two parallel lines}}$
Yes, this is a null set because two parallel lines do not intersect.
Note: A set which does not contain any element is called a null set.
NCERT Question 2 : 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
Solution :
(i) The set of months of a year
Finite — There are $12$ months in a year.
(ii) ${1, 2, 3, \dots}$
Infinite — Set of natural numbers.
(iii) ${1, 2, 3, \dots, 99, 100}$
Finite — Contains $100$ numbers.
(iv) The set of positive integers greater than $100$
Infinite — Positive integers continue endlessly.
(v) The set of prime numbers less than $99$
Finite — Only limited primes below $99$.
Note: A set with a definite number of elements is finite, otherwise infinite.
NCERT Question 3 : State whether each 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)
Solution :
(i) The set of lines parallel to the x-axis
Infinite. We can draw infinite parallel lines with respect to the x-axis.
(ii) The set of letters in the English alphabet
Finite — $26$ letters
(iii) The set of multiples of $5$
Infinite — ${5, 10, 15, \dots}$
(iv) The set of animals living on the earth
Finite — Countable species exist
(v) The set of circles passing through the origin $(0,0)$
Infinite — Different radius possible
NCERT Question 4 : 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 & x ≤ 10}
(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }
Solution :
(i)
Yes. Every element of A is also an element of B and every element of B is also an element of A namely {a, b, c, d}.
Note: Two sets A and B are said to be equal if they have exactly the same elements, and we write A = B. Otherwise, the sets are said to be unequal, and we write A ≠ B. Order in which elements appear does not matter.
$$A = \{a, b, c, d\},\quad B = \{d, c, b, a\}$$
Yes, $A = B$
(ii)
$$A = \{4, 8, 12, 16\},\quad B = \{8, 4, 16, 18\}$$
No. 12 is an element that is present in A but not in B and similarly 18 is an element present in B not in A.
No A ≠ B — $12 \notin B$ and $18 \notin A$
(iii)
$$A =\{2, 4, 6, 8, 10\}$$
$$B = \{x : x \text{ is positive even integer and } x \le 10\}$$
Yes. If we define set B it can be written like this {2, 4, 6, 8, 10} and therefore every element of A is also an element of B and every element of B is also an element of A.
Yes — Both sets represent the same elements
(iv)
$$A = \{x : x \text{ is a multiple of } 10\}$$
$$B = \{10, 15, 20, 25, 30, \dots\}$$
No.If we define B we can clearly see that {-40, -30, -20, -10, 0}. All these numbers are also multiples of 10, and they are not in set B. Hence A ≠ B.
No — $B$ contains numbers not multiples of $10$ and also misses negatives, $0$ etc.
NCERT Question 5 : Are the following pairs of sets equal?
(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}
Solution :
(i)
$$A = \{2, 3\}$$
$$B = \{x : x^2 + 5x + 6 = 0\}$$
Solve the equation:
$$x^2 + 5x + 6 = 0$$
$$(x+2)(x+3) = 0$$
$$x = -2, -3$$
So,
$$B = \{-2, -3\}$$
Not equal — different elements
(ii)
$$A = \{x : x \text{ is a letter in the word FOLLOW}\}$$
$$B = \{y : y \text{ is a letter in the word WOLF}\}$$
Both sets contain:
$$\{F, O, L, W\}$$
Yes — They are equal
NCERT Question 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, a}, G = {1, -1}, H = {0, 1}
Solution :
$A$ and $B$ are said to be equal if they have exactly the same elements.
For $A$,
$8 \in A$, but
$8 \notin B,\ 8 \notin D,\ 8 \notin E,\ 8 \notin F,\ 8 \notin G,\ 8 \notin H$
Hence, $A$ is not equal to $B,\ D,\ E,\ F,\ G,\ H$.
Also,
$2 \in A$, but $2 \notin C$
Hence, $A \ne C$.
For $B$,
$2 \in B$, but
$2 \notin C,\ 2 \notin E,\ 2 \notin F,\ 2 \notin G,\ 2 \notin H$
Hence, $B$ is not equal to $C,\ E,\ F,\ G,\ H$.
Also, every element of $B$ can be found in $D$ namely: $\{1, 2, 3, 4\}$
and vice-versa is also true.
Hence, $B = D$.
For $C$,
$14 \in C$, but
$14 \notin D,\ 14 \notin E,\ 14 \notin F,\ 14 \notin G,\ 14 \notin H$
Hence, $C$ is not equal to $D,\ E,\ F,\ G,\ H$.
For $D$,
$2 \in D$, but
$12 \notin E,\ 2 \notin F,\ 2 \notin G,\ 2 \notin H$
Hence, $D$ is not equal to $E,\ F,\ G,\ H$.
For $E$,
$-1 \in E$, but
$-1 \notin F,\ -1 \notin H$
Hence, $E$ is not equal to $F,\ H$.
Also, every element of $E$ can be found in $G$ namely: $\{-1, 1\}$
and vice-versa is also true.
Hence, $E = G$.
For $F$,
$0 \in F$, but
$0 \notin G,\ 0 \notin H$
Hence, $F$ is not equal to $G,\ H$.
For $G$,
$-1 \in G$, but
$-1 \notin H$
Hence, $G$ is not equal to $H$.
So, we can observe that only:
$$B = D \quad \text{and} \quad E = G$$
Equal pairs:
- $$B = D$$
- $$E = G$$
All other sets differ in at least one element.
FAQs of Chapter-1 Sets Exercise 1.2 NCERT Solutions for Class 11 Maths
What is Exercise 1.2 about?
It focuses on types of sets such as finite, infinite, equal, equivalent, singleton, and empty sets.
What is a finite set?
A set that contains a limited number of elements.
What is an infinite set?
A set that has infinitely many elements.
What is the difference between equal and equivalent sets?
Equal sets have the same elements, while equivalent sets have the same number of elements.
What is a singleton set?
A set that contains exactly one element.
Is the empty set finite or infinite?
The empty set is a finite set with zero elements.
Why is Exercise 1.2 important?
It builds the foundation for understanding subsets and set operations.
Are NCERT solutions enough for this exercise?
Yes, they are sufficient for CBSE exams and helpful for competitive exams.
Important Chapter Links
Sets Exercise 1.2 of Class 11 NCERT Mathematics covers important concepts related to types of sets such as finite and infinite sets, equal sets, equivalent sets, singleton sets, and empty sets. This exercise helps students understand how to classify sets based on their elements and properties. With clear explanations and solved questions, it strengthens the foundation required for topics like subsets and set operations. It is highly useful for CBSE exams and competitive exams like JEE, NDA, IMUCET, and Merchant Navy entrance exams.
Exercise-wise NCERT Solutions
- Basic definition of sets
- Writing sets in roster and set-builder form
Exercise 1.2
- Types of sets
- Finite and infinite sets
- Subsets and proper subsets
- Number of subsets
- Set operations (union, intersection, complement)
- Advanced problems on set operations and Venn diagrams
- Mixed problems covering all concepts of the chapter