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# NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.5 - PDF Download

JEE Mains & Advanced

NCERT solutions class 11 math chapter 1 sets ex 1.5 based on the questions that cover the topic complement of a set. The questions included in these solutions are effective in testing the students’ understanding of concepts while also reinforcing their problem solving abilities. Class 11 maths chapter 1 exercise 1.5 NCERT solutions consist of 7 questions associated with the complement of a set. NCERT solutions for class 11 maths chapter 1 ex 1.5 are developed by subject experts of eSaral.  These solutions provide a deep understanding of each question with step by step solutions.

Ex 1.5 class 11 maths chapter 1 solutions are available on eSaral in free PDF format that will help you to prepare for examination. To achieve a high score in the exam, you can download the PDF from the eSaral website.

## Topics Covered in Exercise 1.5 Class 11 Mathematics Questions

Ex 1.5 class 11 maths chapter 1 sets are about solving questions on the topic complement of a set. The detailed solutions are provided here by eSaral’s experts for the topic complement of a set.

 1 Complement of a Set
1. Complement of a Set - Let U be the universal set and A a subset of U. Then the complement of A is the set of all elements of U which are not the elements of A. Symbolically, we write A′ to denote the complement of A with respect to U. thus,

A′ = {x : x ∈ U and x ∉ A }. Obviously A′ = U – A

The complement of a set A can be looked upon, alternatively, as the difference between a universal set U and the set A.

The complement of the union of two sets is the intersection of their complements and the complement of the intersection of two sets is the union of their complements. These are called De Morgan’s laws.

The complement A′ of a set A can be represented by a Venn diagram.

Some Properties of Complement Sets

• Complement laws: (i) A ∪ A′ = U (ii) A ∩ A′ = ϕ

• De Morgan’s law: (i) (A ∪ B)´ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′

• Law of double complementation : (A′)′ = A

• Laws of empty set and universal set ϕ′ = U and U′ = ϕ.

These laws can be verified by using Venn diagrams.

## Tips for Solving Exercise 1.5 Class 11 Chapter 1 Sets

This exercise includes all the required topics regarding the properties of complement of sets. Each of these topics can be learned by doing all the questions in detail and following the tips given by the subject experts of eSaral that are included in NCERT solutions class 11 maths chapter 1 ex 1.5.

1. Ex 1.5 is one of the essential exercises that you need to learn because the knowledge provided in the NCERT solutions class 11 maths chapter 1 ex 1.5 helps you in developing a comprehensive understanding of all the concepts.

2. There are 4 significant laws that students can use to try out the exercise questions that you must remember.

3. It is important to have a good understanding of all the concepts and properties involved in ex 1.5 in order to solve the tricky questions asked in this exercise.

## Importance of Solving Ex 1.5 Class 11 Maths Chapter 1 Sets

There are different kinds of benefits for referring to the NCERT solutions class 11 maths chapter 1 ex 1.5. You can find these benefits mentioned below.

1. Venn’s diagram is the basis for every property of complement of set that you have encountered in this chapter. This will help you to understand the questions of ex 1.5.

2. Using venn’s diagram, you can attempt to prove all the complements of sets. It will construct your basic set and its properties.

3. In NCERT solutions class 11 maths chapter 1 ex 1.5, we have also provided some examples and important questions that will give you a clear understanding of concepts.

4. These solutions are available in PDF format which students can download anytime and practice questions for preparing exams.

#### Frequently Asked Questions

Question 1. What is the complement of a set?

Answer 1. Let U be the universal set and A a subset of U. Then the complement of A is the set of all elements of U which are not the elements of A. Symbolically, we write A′ to denote the complement of A with respect to U. thus,  A′ = {x : x ∈ U and x ∉ A }. Obviously A′ = U – A

Question 2. Write some properties of complement sets?

Answer 2. There are some properties of complement sets.

• Complement laws: (i) A ∪ A′ = U (ii) A ∩ A′ = φ

• De Morgan’s law: (i) (A ∪ B)´ = A′ ∩ B′ (ii) (A ∩ B)′ = A′ ∪ B′

• Law of double complementation : (A′)′ = A

• Laws of empty set and universal set φ′ = U and U′ = φ.