You can Practice Various problems involving Set Operations here. Use them to learn different operations such as Union, Intersection, Complement, etc. We are sure by the end of this article you will be familiar with the Operations on Sets through the Problems Provided. Sets Questions and Answers here help you to understand the Operations concept much easier. If you need more help refer to **Set Theory** and learn the entire concept of Sets.

## Sets Questions and Answers

1. Let A and B be two finite sets such that n(A) = 15, n(B) = 24 and n(A ∪ B) = 30, find n(A ∩ B)?

Solution:

n(A U B) = n(A) + n(B) – n(A ∩ B)

Rearranging we get the n(A ∩ B) = n(A) + n(B) – n(A ∪ B)

= 15+24 – 30

= 9

2. If n(A – B) = 28, n(A ∪ B) = 80 and n(A ∩ B) = 35, then find n(B)?

Solution:

Using the formula n(A∪B) = n(A – B) + n(A ∩ B) + n(B – A)

80 = 28 + 35 + n(B – A)

80 = 63 + n(B – A)

n(B – A) = 80 – 43

n(B – A) = 37

Now n(B) = n(A ∩ B) + n(B – A)

= 35 + 37

= 72

3. If n(U) = 28, n(A) = 14, n (AnB) = 10, n(B’) = 22 find n(AUB)?

Solution:

n (A U B) = n (A) + n (B) – n (A n B)

n (B) = n (U) – n (B’)

= 28 – 22

= 6

n (A U B) = n (A) + n (B) – n (A n B)

= 14+6 – 10

= 10

Thus, the value of n (A U B) = 10.

4. If A = { a, b } and B = { 3, 4 }. What is the Cartesian Product of Two Sets AxB and Bx A. Verify whether they are equal or not?

Solution:

Cartesian Product AxB = { (a, 3), (a, 4), (b, 3), (b, 4)}

BxA = { (3, a), (4, a), (3, b), (4, b)}

Therefore, AxB ≠ BxA

5. If A = {12, 13, 14, 15, 16, 17 } and B = {7, 8, 9}, then find the values of (A – B) and (B-A)?

Solution:

Given A = {12, 13, 14, 15, 16, 17 }

B = {7, 8, 9}

A-B = {12, 13, 14, 15, 16, 17 } – {7, 8, 9}

= {12, 13, 14, 15, 16, 17}

12, 13, 14, 15, 16, 17 are the elements that are present in A but not in B.

B-A = {7, 8, 9} – {12, 13, 14, 15, 16, 17}

= {7, 8, 9}

6. If If A = {10, 11, 12, 13, 14 } and B = { 10, 12, 14, 15 }. Find A ∩ B?

A ∩ B = {10, 11, 12, 13, 14 } ∩ { 10, 12, 14, 15 }

= { 10, 12, 14}

A ∩ B contains all the elements that are in both Sets A and B.

7. Let A = {2, 3, 4}, B = {3, 4, 5} , U = { 1, 2, 3, 4, 5} find the Complement of A and B?

Solution:

Given

A = {2, 3, 4}

B = {3, 4, 5}

U = {1, 2, 3, 4, 5}

A^{c} or A^{‘} = U – A

= {1, 2, 3, 4, 5} – {2, 3, 4}

={ 1, 5}

B^{c} or B^{‘} = U – B

= {1, 2, 3, 4, 5} – {3, 4, 5}

{ 1, 2}