Table of Content

• Formulas on Operations on Sets
• Practice Questions on Operations on Sets
• Practice Questions on Operations on Sets with Solution
• FAQs on Operations of Sets

Operation on Set	Description
Union of Set	A ∪ B = All the elements present in A and B
Intersection of Set	A ∩ B = Common element in A and B
Difference of Set	A – B = Elements belongs to A but not B
Complement of Set	Ac = U – A
Number of Elements in a Set	n(A∪B) = n(A) + n(B) – n(A∩B)

Practice Questions on Operations on Sets – Solved

These practice questions on operations on sets are designed to enhance your understanding of key concepts such as union, intersection, difference, and complement.

1. Find the union of set A and B given that set A = {2, 4, 6} and set B = {4, 10}.

A = {2, 4, 6}

B = {4, 10}

A ∪ B = {2, 4, 6, 10}

2. Find the intersection of set X and Y given X = {5, 9, 10, 15} and Y = {4, 5, 12}.

X = {5, 9, 10, 15}

Y = {4, 5, 12}

X ∩ Y = {5}

3. Find the complement of set P given the universal set U = {10, 20, 30, 40, 50, 60} and P = {20}.

U = {10, 20, 30, 40, 50, 60}

P = {20}

P^c = U – P

P^c = {10, 20, 30, 40, 50, 60} – {20}

P^c = {10, 30, 40, 50, 60}

4. Find the set difference of sets C and D given that C = {1, 4, 7} and D = {4, 8}

C = {1, 4, 7}

D = {4, 8}

C – D = {1, 4, 7} – {4, 8}

C – D = {1, 7}

5. Find the power set of the set A = {2, 7}

A = {2, 7}

Power set of A = P(A) = {?, 2, 7, {2,7}}

6. What are the number of elements in the union of two sets P and Q with number of elements 5, 6 respectively. Also, the number of common elements in both sets is 2.

n(A∪B) = n(A) + n(B) – n(A∩B)

n(A∪B) = 5 + 6 – 2

n(A∪B) = 9

7. Find the number of elements in the intersection of two sets given the number of elements of sets U and V are 8 and 9 and the number of elements in their union is 13.

n(A∩B) = n(A) + n(B) – n(A∪B)

n(A∩B) = 8 + 9 – 13

n(A∩B) = 4

Practice Questions on Operations on Sets – Unsolved

1. Find the union of set A and B given that set A = {1, 2, 5} and set B = {7, 9}.

2. Find the intersection of set X and Y given X = {1, 4} and Y = {3, 4, 5}.

3. Find the complement of set P given the universal set U = {1, 2, 3, 4, 5, 6} and P = {2, 5}.

4. Find the set difference of sets C and D given that C = {10, 20, 30} and D = {1, 10}

5. Find the power set of the set A = {1, 4}

6. What are the number of elements in the union of two sets P and Q with number of elements 10, 8 respectively. Also the number of common elements in both sets is 3.

7. Find the number of elements in the intersection of two sets given the number of elements of sets U and V are 5 and 7 and the number of elements in their union is 10.

Practice Questions on Operations on Sets – FAQs

What is difference of set?

Difference of sets refers to the elements that are present in one set but not in another. Let A and B bet two set, the difference of A, and B (denoted as [Tex] A−B or A \setminus B )[/Tex] .

Example: [Tex]A = \{1,2,3,4\} \ and \ B = \{3,4,5,6\} [/Tex]

then: [Tex]A -B = \{1,2\}[/Tex]

What are the 4 Types of Set Operations?

The 4 types of set operations include union, intersection, difference and complement.

What does ∩ and ∪ Mean in Math?

‘∩’ represents the intersection of the sets A and B, whereas, ‘∪’ represents the Union of the sets A and B.

What are the Properties of Sets and Operations?

There are six properties of sets that are:

• Commutative Property
• Associative Property
• Distributive Property
• Identity Property
• Complement Property
• Idempotent Property