Sets questions with solutions are given here for students to make them understand the concept easily. Practising these problems will help to go through the concept of sets theory. It is an important chapter for Class 11 students, hence we have given the questions based on the NCERT curriculum, with respect to the CBSE syllabus.

A brief introduction for each sub-topic of sets is also provided so that students can solve the questions quickly. Some of the basic definitions related to this concept are given below. Also, read Sets For Class 11, here.

Sets: A collection of well-defined objects. It is denoted by capital letters.

Example: A = {1, 2, 3, 4, 5..}. Set A is a collection of all natural numbers.

Roster form of sets: All elements are written in curly braces { }, separated by commas.

Example: R = {1, 3, 7, 21, 2, 6, 14, 42}.

Set Builder Form: The elements of the set represent a common property.

Example, R = {x : x is a vowel in English alphabet}

First, let us see some questions based on the representation of sets.

Questions on Sets with Solutions

1. Write the solution set of the equation x² – 4=0 in roster form.

Solution: x² – 4 = x² – 2² = (x-2) (x+2)

x=2,-2

Thus, A = {-2,2}

2. Write the set A = {1, 4, 9, 16, 25, . . . } in set-builder form.

Solution: If we see the pattern here, the numbers are squares of natural numbers, such as:

1² = 1

2² = 4

3² = 9

4² = 16

And so on.

A = {x : x is the square of a natural number}

Or we can write;

A = {x : x = n² , where n ∈ N}

3. Write an example of a finite and infinite set in set builder form.

Solution:

Finite set, A = {x : x ∈ N and (x – 1) (x –2) = 0}

Infinite Set, B = {x : x ∈ N and x is prime}

4. Write an example of equal sets.

Solution: Let there be two sets A and B

A is the set of letters in “ALLOY”

B is the set of letters in “LOYAL”

Hence,

A = {A,L,L,O,Y}

B = {L,O,Y,A,L}

Therefore, in both sets, the elements are the same.

So, A = B.

5. Write the subsets of {1,2,3}.

Solution: Let A = {1,2,3}

The subsets of A are: φ, {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3}

6. Write {x: x ∈ R, 3 ≤ x ≤ 4} as intervals.

Solution: {x: x ∈ R, 3 ≤ x ≤ 4} = [3, 4]

7. Write the interval (6, 12) in set builder form.

Solution:

Let A be the interval (6, 12)

The interval (6, 12) in set builder form is

A={x: x ∈ R, 6 < x < 12}

8. If set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then write the universal set for all three sets.

Solution: If U is the universal set for sets A, B and C, then:

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Also, read: Sets Subset And Superset

9. If A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∪ B.

Solution: A ∪ B = { 2, 4, 6, 8, 10, 12}

10. If A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∩ B.

Solution: A ∩ B = { 6, 8 }

Also, see: Operation On Sets Intersection Of Sets And Difference Of Two Sets

11. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}. Find A ∪ B ∪ C.

Solution: A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}

12. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15}. Find A ∩ (B ∪ C).

Solution: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

= {7, 9, 11} ∪ {11}

= {7, 9, 11}

13. If A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find A – B and B – A.

Solution: A – B = { 1, 3, 5 }

B – A = { 8 }

Clearly, A – B ≠ B – A

14. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}. Find A′.

Solution: A′ = { 2, 4, 6, 8,10 }

Practice Questions

Solve the following questions on sets:

1. Check whether the given sets are equal sets: A = {1, 2, 3, 4} and B = {2, 4, 1, 3}.
2. Write the subsets for the set A = {1, 3, 5, 7}
3. Write the set A = {1, 2, 3, 4, 5, …} in set-builder form.
4. If A = {1, 3, 5, 7, 9, 11} and B = {1, 2, 3, 13}, the find A-B and B-A.
5. Find A∪(B∪C), if A = {1, 3, 5}, B = {2, 4, 6} and C = {1, 5, 7}.

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