Arpita Srivastava Content Writer
Content Writer | Updated On - Jul 25, 2025
Sets are an important topic covered in chapter 1 of NCERT Class 11 Mathematics. They are described as a collection of elements or members of different kinds.
- Sets can be created in the roster-form and set-builder form.
- It consists of a finite as well as an infinite number of elements.
- The set theory is an important component in the mathematical classification and organization of data.
- A German mathematician named Georg Cantor coined the term.
- Each member of the set theory in Mathematics is called an element.
- Cardinal numbers are defined as the number of elements found in the set.
- Each element found is represented by a curly bracket.
- The collection of plates and the children's school books are all examples of sets.
There are four main operations performed on the set, which are as follows:
- Union of Sets (∪)
- Intersection of Sets (∩)
- Difference of Sets (–)
- Complement of a Set (A′ or Ac)
Sets MCQs
Ques. Write X = {1, 2, 3, 5, 7,…} in set builder form.
- X = {x: x is a set of prime numbers}
- X = {x: x is a set of whole numbers}
- X = {x: x is a set of natural numbers}
- X = {x: x is a set of square numbers}
Click here for the answer
Ans. (a) X = {x: x is a set of prime numbers}
Explanation: Given, X = {1, 2, 3, 5, 7,…}
∵ These are prime numbers
∴ X = {x: x is a set of prime numbers}
Ques. Write the solution set of the equation x2 - 4x – 4 = 0 in roster form.
- 1,2
- 2,2
- 3,2
- 4,2
Click here for the answer
Ans. (b) (2,2)
Explanation: The given equation is a quadratic equation.
∴ On factoring the given equation x2 - 4x – 4 = 0, we get
⇒ x2- 2(2x) - (2)2 = 0
⇒ (x - 2) (x - 2) = 0
Thus, x = 2 or x = 2
∴ the solution set of the equation x2 - 4x – 4 = 0 in roster form is {2,2}.
Ques. If A and B are two finite sets such that n(A) = 25, n(B) = 30, and n(A ∪ B) = 30, find n(A ∩ B).
- 10
- 25
- 33
- 42
Click here for the answer
Ans. (b) 25
Explanation: Using the formula, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒ n(A ∩ B) = n(A) + n(B) – n(A ∪ B)
= 25 + 30 – 30
∴ 25
Ques. What will be the given set in a set-builder form: A = {3, 6, 9, 12, 15, 18, 21}?
- A = {x | x is multiple of three}
- A = {x | x is multiple of four}
- A = {x | x is multiple of five}
- A = {x | x is multiple of six}
Click here for the answer
Ans. (a) A = {x | x is multiple of three}
Explanation: The set is given as A = {3, 6, 9, 12, 15, 18, 21}
∴ It can be represented in Set-Builder form as follows:
∴ A = {x | x is multiple of three}
Ques. If A and B are two finite sets such that n(A) = 15, n(B) = 30, and n(A ∪ B) = 20, find n(A ∩ B).
- 10
- 25
- 33
- 42
Click here for the answer
Ans. (b) 25
Explanation: Using the formula, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒ n(A ∩ B) = n(A) + n(B) – n(A ∪ B)
= 15 + 30 – 20
∴ 25
Ques. What will be the intersection of Sets: Set A = {1,2,3,4} and Set B = {3,4,5}?
- {3,4}
- {3,4,6}
- {3,4,2}
- {3,4,1}
Click here for the answer
Ans. (a) {3,4}
Explanation: Given Sets are:
∵ Set A = {1,2,3,4}
∵ Set B = {3,4,5}
∴ Intersection of Sets will be, A ∩ B = {3,4} as 3 and 4 exists in both sets A and B.
Ques. What will be the union of sets: Set A = {1,2,3,4,9} and Set B = {6,7,8}?
- {1,2,3,4,6,7,9}
- {1,2,4,6,7,8,9}
- {1,2,3,4,8,9}
- {1,2,3,4,6,7,8,9}
Click here for the answer
Ans. (d) {1,2,3,4,6,7,8,9}
Explanation: Given Sets are:
∵ Set A = {1,2,3,4}
∵ Set B = {6,7}
∴ Union of Sets will be, A ∪ B = {1,2,3,4,6,7,8,9}.
Ques. What will be the difference between Sets: Set A = {1,4,5,6,7} and Set B = {6,7}?
- {1,4,5,7}
- {1,4,5,8}
- {1,4,5}
- {1,4,5,9}
Click here for the answer
Ans. (c){1,4,5}
Explanation: Given Sets are:
∵ Set A = {1,2,3,4,5,6,7}
∵ Set B = {6,7}
∴ Difference of Sets will be given as: (A-B) = {}
∴ A – B = {1,4,5}
Ques. Find the complement of a set A when U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 3, 4}.
- {2, 5, 6, 7, 8, 9}
- {2, 6, 7, 8, 9}
- {2, 5, 6, 7, 8}
- { 6, 7, 8, 9}
Click here for the answer
Ans. (a) {2, 5, 6, 7, 8, 9}
Explanation: Given Sets are:
∵ U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
∵ A = {1, 3, 4}
Thus, the complement of Set A will be
∴ A' = {2, 5, 6, 7, 8, 9}
Ques. If n(A - B) = 10, n(A ∪ B) = 60 and n(A ∩ B) = 20, then find n(B).
- 10
- 20
- 30
- 50
Click here for the answer
Ans. (d) 50
Explanation: Using the formula n(A∪B) = n(A - B) + n(A ∩ B) + n(B - A)
⇒ 60 = 10 + 20 + n(B - A)
⇒ 60 = 30 + n(B - A)
⇒ n(B - A) = 60 - 30
⇒ n(B - A) = 30
Now n(B) = n(A ∩ B) + n(B - A)
= 20 + 30
∴ 50
Ques. In a group of 60 people, 20 prefer cold beverages and 56 prefer hot beverages, and each prefers at least one of the two. How many people like coffee and tea?
- 16
- 20
- 3
- 34
Click here for the answer
Ans. (a) 16
Explanation: Let A represent a group of people who enjoy drinking cold beverages.
∵ B = A group of people who enjoy hot beverages.
Given
⇒ (A ∪ B) = 60 n(A) = 20 n(B) = 30 then;
⇒ n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
⇒ 56 + 20 - 60
⇒ 76 - 60 = 16
∴ 16
Therefore, 16 people like both tea and coffee.
Ques. If A and B are two finite sets such that n(A) = 25, n(B) = 25, and n(A ∪ B) = 20, find n(A ∩ B).
- 10
- 25
- 30
- 42
Click here for the answer
Ans. (c) 30
Explanation: Using the formula, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒ n(A ∩ B) = n(A) + n(B) – n(A ∪ B)
⇒ 25 + 25 – 20
∴ 30
Ques. What will be the intersection of Sets: Set A = {2,3} and Set B = {3,4,5}?
- {3}
- {3,4,6}
- {3,4,2}
- {3,4,1}
Click here for the answer
Ans. (a) {3}
Explanation: Given Sets are:
∵ Set A = {2,3}
∵ Set B = {3,4,5}
∴ Intersection of Sets will be, A ∩ B = {3} as 3 exists in both sets A and B.
Ques. What will be the union of sets: Set A = {1,2,3,4,9,10} and Set B = {6,7,8,11}?
- {1,2,3,4,6,7,9}
- {1,2,4,6,7,8,9}
- {1,2,3,4,8,9}
- {1,2,3,4,6,7,8,9,10,11}
Click here for the answer
Ans. (d) {1,2,3,4,6,7,8,9,10,11}
Explanation: Given Sets are:
∵ Set A = {1,2,3,4,9,10}
∵ Set B ={6,7,8,11}
∴ Union of Sets will be, A ∪ B = {1,2,3,4,6,7,8,9,10,11}.
Ques. What will be the difference between Sets: Set A = {1,4,5,6,7,2,9} and Set B = {6,7,2}?
- {1,4,5,7}
- {1,4,5,8,3}
- {1,4,5,9}
- {1,4,5,9,2}
Click here for the answer
Ans. (c){1,4,5,9}
Explanation: Given Sets are:
∵ Set A = {1,4,5,6,7,2,9}
∵ Set B = {6,7}
∴ Difference of Sets will be given as: (A-B) = {}
∴ A – B = {1,4,5,9}
Ques. In a group of 100 people, 120 prefer cold beverages and 50 prefer hot beverages, and each prefers at least one of the two. How many people like coffee and tea?
- 70
- 20
- 30
- 34
Click here for the answer
Ans. (a) 70
Explanation: Let A represent a group of people who enjoy drinking cold beverages.
∵ B = A group of people who enjoy hot beverages.
Given
⇒ (A ∪ B) = 100 n(A) = 120 n(B) = 50 then;
⇒ n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
= 120 + 50 - 100
= 70
∴ 70 people like both tea and coffee.
For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates
Check-Out:
Comments