Problems on Complement of a Set | Complement of a Set Questions and Answers

In this article, you will learn how to find the Complement of a Set. Check out the below sections to get an idea of how to find the Complement of a Set. Refer to Questions on Complement of a Set along with Answers explained in detail and get a grip on the concept. To learn completely about various operations on sets have a glance at the Set Theory and get a good hold of all the underlying topics.

Solved Example Questions on Complement of a Set

1. If U = {2, 4, 6, 8, 10, 12, 14} and A = {1, 3, 5}. Find the Complement of A?

Solution:

A^c or A^‘ = U – A

= {2, 3, 4, 5, 6, 8, 10, 12, 14} – {1, 3, 5}

= { 2, 4, 6, 8, 10, 12, 14}

The Complement of A is the Elements that are in the Universal Set and not in the Set A.

2. Given Sets B = {1 Orange, 1 Pineapple, 1 Guava, 1 Pomegranate} and U = {1 Guava, 1 Orange, 1 Apricot, 1 Pomegranate, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit }. Find the Complement of B?

Solution:

B = {1 Orange, 1 Pineapple, 1 Guava, 1 Pomegranate}

U = {1 Guava, 1 Orange, 1 Apricot, 1 Pomegranate, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit }

B^c or B^‘ = U – B

= {1 Guava, 1 Orange, 1 Apricot, 1 Pomegranate, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit } – {1 Orange, 1 Pineapple, 1 Guava, 1 Pomegranate}

= { 1 Apricot, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit}

3. Find the Complement of B if the Sets are B = {1, 3, 4, 5} U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }?

Solution:

Given Sets are

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

B = {1, 3, 4, 5}

B^c or B^‘ = U – B

= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 3, 4, 5}

= {2, 6, 7, 8, 9}

4. Find the Complement of A

A = { x / x is a number bigger than 6 and smaller than 10}

U = { x / x is a positive number smaller than 10}

Solution:

Given

A = { x / x is a number bigger than 6 and smaller than 10}

= { 7, 8, 9}

U = { x / x is a positive number smaller than 10}

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

A^c or A^‘ = U – A

= { 1, 2, 3, 4, 5, 6, 7, 8, 9 } – { 7, 8, 9}

= {1, 2, 3, 4, 5, 6}

5. Let U = {x : x is an integer, –7 ≤ x ≤ 4}, P = {-4, -2, 0, 7, 8, 9, 6}. Find the Complement of P?

Solution:

P = {-4, -2, 0, 7, 8, 9, 6}

U = {x : x is an integer, –7 ≤ x ≤ 4}

U = {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}

P^c or P^‘ = U – P

= {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4} – {-4, -2, 0, 7, 8, 9, 6}

= { -7, -6, -5, -3, -1, 1, 2, 3, 4}