Practice Questions on Operations on Sets

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

Solved Examples

Q1. 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}

Q2. 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}

Q3. 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}

Q4. 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}

Q5. Find the power set of the set A = {2, 7}

A = {2, 7}

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

Q6. 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

Q7. 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

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.

Answer Key:

1. {1, 2, 5, 7, 9}

2. {4}

3. {1, 3, 4, 6}

4. {20, 30}

5. {\phi , {1} , {4}, {1, 4}}

6. 15

7. 2