NCERT Solutions for Exercise 1.4 Class 11 Maths Chapter 1 - Sets

# NCERT Solutions for Exercise 1.4 Class 11 Maths Chapter 1 - Sets

Edited By Vishal kumar | Updated on Nov 01, 2023 09:49 AM IST

## NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.4- Download Free PDF

In the previous exercises of this chapter, you have already learned about the definition of sets, representation of sets, subsets, power sets, universal sets, etc. In the NCERT solutions for Class 11 Maths Chapter 1 Exercise 1.4, you will learn about the Venn Diagrams. It is a very important concept used to define the relationships between sets using diagrams. These diagrams consist of a rectangle and closed curves.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics WallahAakash Unacademy

The rectangle represents the universal set and the closed curves inside the rectangle represent the subsets. Operations on sets like the union of sets, the intersection of sets, the properties of the union of sets, and the properties of the intersection of sets are also covered in the Class 11 Maths chapter 1 exercise 1.4 solutions. The other important topic difference of sets is also covered in exercise 1.4 Class 11 Maths. These topics are very important which are useful in this chapter as well as in other chapters like relations and functions, probability, etc. If you are looking for NCERT Solutions, you can click on the given link to get NCERT solutions for Classes 6 to 12.

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## Access sets Class 11 Chapter 1 Exercise: 1.4

X = {1, 3, 5} Y = {1, 2, 3}

Union of X and Y is X $\cup$ Y = {1,2,3,5}

Question:1(ii) Find the union of each of the following pairs of sets :

A = [ a, e, i, o, u} B = {a, b, c}

Union of A and B is A $\cup$ B = {a,b,c,e,i,o,u}.

Question:1(iii) Find the union of each of the following pairs of sets :

A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}

Here ,

A = {3,6,9,12,15,18,............}

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

Union of A and B is A $\cup$ B.

A $\cup$ B = {1,2,3,4,5,6,9,12,15........}

Question:1(iv) Find the union of each of the following pairs of sets :

A = {x : x is a natural number and 1 $<$ x $\leq$6 }

B = {x : x is a natural number and 6 $<$ x $<$10 }

Here,

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

B = {7,8,9}

A $\cup$ B = {2,3,4,5,6,7,8,9}

or it can be written as A $\cup$ B = {x : x is a natural number and 1$<$ x $<$10 }

A = {1, 2, 3} B = $\phi$

Here,

A union B is A $\cup$ B.

A $\cup$ B = {1,2,3}

Here,

We can see elements of A lie in set B.

Hence, A $\subset$ B.

And, A $\cup$ B = {a,b,c} = B

If A is subset of B then A $\cup$ B will be set B.

A $\cup$ B

Here,

A = {1, 2, 3, 4}

B = {3, 4, 5, 6}

The union of the set can be written as follows

A $\cup$ B = {1,2,3,4,5,6}

A $\cup$ C

Here,

A = {1, 2, 3, 4}

C = {5, 6, 7, 8 }

The union can be written as follows

A $\cup$ C = {1,2,3,4,5,6,7,8}

B $\cup$ C

Here,

B = {3, 4, 5, 6},

C = {5, 6, 7, 8 }

The union of the given sets are

B $\cup$ C = { 3,4,5,6,7,8}

B $\cup$ D

Here,

B = {3, 4, 5, 6}

D = { 7, 8, 9, 10 }

B $\cup$ D = {3,4,5,6,7,8,9,10}

A $\cup$ B $\cup$ C

Here,

A = {1, 2, 3, 4},

B = {3, 4, 5, 6},

C = {5, 6, 7, 8 }

The union can be written as

A $\cup$ B $\cup$ C = {1,2,3,4,5,6,7,8}

A $\cup$ B $\cup$ D

Here,

A = {1, 2, 3, 4},

B = {3, 4, 5, 6}

D = { 7, 8, 9, 10 }

The union can be written as

A $\cup$ B $\cup$ D = {1,2,3,4,5,6,7,8,9,10}

B $\cup$ C $\cup$ D

Here,B = {3, 4, 5, 6},

C = {5, 6, 7, 8 } and

D = { 7, 8, 9, 10 }

The union can be written as

B $\cup$ C $\cup$ D = {3,4,5,6,7,8,9,10}

(i) X = {1, 3, 5} Y = {1, 2, 3}

(ii) A = [ a, e, i, o, u} B = {a, b, c}

(iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}

(iv) A = {x : x is a natural number and 1 $<$x $\leq$6 } B = {x : x is a natural number and 6 $<$ x $<$ 10 }

(v) A = {1, 2, 3}, B = $\phi$

(i) X = {1, 3, 5} Y = {1, 2, 3}

X $\cap$ Y = {1,3}

(ii) A = [ a, e, i, o, u} B = {a, b, c}

A $\cap$ B = {a}

(iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}

A = {3,6,9,12,15.......} B = {1,2,3,4,5}

A $\cap$ B = {3}

(iv)A = {x : x is a natural number and 1 $<$x $\leq$6 } B = {x : x is a natural number and 6 $<$ x $<$ 10 }

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

A $\cap$ B = $\phi$

(v) A = {1, 2, 3}, B = $\phi$

A $\cap$ B = $\phi$

(i) A $\cap$ B (ii) B $\cap$ C

(iii) A $\cap$C $\cap$ D (iv) A $\cap$ C

(v) B $\cap$ D (vi) A $\cap$ (B $\cup$ C)

(vii) A $\cap$ D (viii) A $\cap$ (B $\cup$ D)

(ix) ( A $\cap$ B ) $\cap$ ( B $\cup$ C ) (x) ( A $\cup$ D) $\cap$ ( B $\cup$ C)

Here, A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

(i) A $\cap$ B = {7,9,11} (vi) A $\cap$ (B $\cup$ C) = {7,9,11}

(ii) B $\cap$ C = { 11,13} (vii) A $\cap$ D = $\phi$

(iii) A $\cap$C $\cap$ D = $\phi$ (viii) A $\cap$ (B $\cup$ D) = {7,9,11}

(iv) A $\cap$ C = { 11 } (ix) ( A $\cap$ B ) $\cap$ ( B $\cup$ C ) = {7,9,11}

(v) B $\cap$ D = $\phi$ (x) ( A $\cup$ D) $\cap$ ( B $\cup$ C) = {7,9,11,15}

(i) A $\cap$ B

(ii) A $\cap$ C

(iii) A $\cap$ D

(iv) B $\cap$ C

(v) B $\cap$ D

(vi) C $\cap$ D

Here, A = {1,2,3,4,5,6...........}

B = {2,4,6,8,10...........}

C = {1,3,5,7,9,11,...........}

D = {2,3,5,7,11,13,17,......}

(i) A $\cap$ B = {2,4,6,8,10........} = B

(ii) A $\cap$ C = {1,3,5,7,9.........} = C

(iii) A $\cap$ D = {2,3,5,7,11,13.............} = D

(iv) B $\cap$ C = $\phi$

(v) B $\cap$ D = {2}

(vi) C $\cap$ D = {3,5,7,11,13,..........} = $\left ( x:x \, is\, \, odd\, \, \, prime \, \, number \right )$

Question:8(i) Which of the following pairs of sets are disjoint

{1, 2, 3, 4} and {x : x is a natural number and 4 $\leq$x $\leq$6 }

Here, {1, 2, 3, 4} and {4,5,6}

{1, 2, 3, 4} $\cap$ {4,5,6} = {4}

Hence,it is not a disjoint set.

Question:8(ii) Which of the following pairs of sets are disjoint

{ a, e, i, o, u } and { c, d, e, f }

Here, { a, e, i, o, u } and { c, d, e, f }

{ a, e, i, o, u } $\cap$ { c, d, e, f } = {e}

Hence,it is not disjoint set.

Question:8(iii) Which of the following pairs of sets are disjoint

{x : x is an even integer } and {x : x is an odd integer}

Here, {x : x is an even integer } and {x : x is an odd integer}

{2,4,6,8,10,..........} and {1,3,5,7,9,11,.....}

{2,4,6,8,10,..........} $\cap$ {1,3,5,7,9,11,.....} = $\phi$

Hence,it is disjoint set.

(i) A – B (ii) A – C (iii) A – D (iv) B – A (v) C – A (vi) D – A

(vii) B – C (viii) B – D (ix) C – B (x) D – B (xi) C – D (xii) D – C

A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }

The given operations are done as follows

(i) A – B = {3,6,9,15,18,21} (vii) B – C = {20}

(ii) A – C = {3,9,15,18,21} (viii) B – D = {4,8,12,16}

(iii) A – D = {3,6,9,12,18,21} (ix) C – B = {2,6,10,14}

(iv) B – A = {4,8,16,20} (x) D – B = {5,10,15}

(v) C – A = {2,4,8,10,14,16} (xi) C – D = {2,4,6,8,12,14,16}

(vi) D – A = {5,10,20} (xii) D – C = {5,15,20}

(i) X – Y

(ii) Y – X

(iii) X $\cap$ Y

X= { a, b, c, d } and Y = { f, b, d, g}

(i) X – Y = {a,c}

(ii) Y – X = {f,g}

(iii) X $\cap$ Y = {b,d}

R = set of real numbers.

Q = set of rational numbers.

R - Q = set of irrational numbers.

{ 2, 3, 4, 5 } and { 3, 6} are disjoint sets.

Here,

{ 2, 3, 4, 5 } and { 3, 6}

{ 2, 3, 4, 5 } $\cap$ { 3, 6} = {3}

Hence,these are not disjoint sets.

So,false.

{ a, e, i, o, u } and { a, b, c, d }are disjoint sets

Here, { a, e, i, o, u } and { a, b, c, d }

{ a, e, i, o, u } $\cap$ { a, b, c, d } = {a}

Hence,these are not disjoint sets.

So, statement is false.

{ 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.

Here,

{ 2, 6, 10, 14 } and { 3, 7, 11, 15}

{ 2, 6, 10, 14 } $\cap$ { 3, 7, 11, 15} = $\phi$

Hence, these are disjoint sets.

So,given statement is true.

{ 2, 6, 10 } and { 3, 7, 11} are disjoint sets.

Here,

{ 2, 6, 10 } and { 3, 7, 11}

{ 2, 6, 10 } $\cap$ { 3, 7, 11} = $\phi$

Hence,these are disjoint sets.

So,statement is true.

## More About NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.4:-

Class 11th Maths chapter 1 exercise 1.4 consists of questions related to finding the unions, intersections, differences of sets using Venn's diagram. There are some definitions and properties of these operations on sets is given before the Class 11 Maths ch 1 ex 1.4. You must go through these properties and examples in order to understand the concept. A total of 12 questions are given in the NCERT book exercise 1.4 Class 11 Maths which are based on the operations on sets. You should try to solve these exercise questions by yourself to get a command on this ex 1.4 class 11.

Also Read| Sets Class 11th Notes

## Benefits of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.4:-

• NCERT Syllabus Class 11th Maths chapter 1 exercise 1.4 is important to get conceptual clarity about Venn's diagram which is a very important concept for solving problems related to relationships between sets, probability.
• You may not be able to solve these exercise problems by yourself at first, you can take help from the Class 11 Maths chapter 1 exercise 1.4 solutions.
• Class 11th Maths chapter 1 exercise 1.4 solutions give you different ways to approach the problems.
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## Key Features of NCERT 11th Class Maths Exercise 1.4 Answers

1. Expertly Crafted Solutions: The ex 1.4 class 11 solutions are prepared by subject experts with a deep understanding of mathematical concepts and the CBSE curriculum.

2. Alignment with CBSE Syllabus: The class 11 maths ex 1.4 solutions are in accordance with the latest CBSE syllabus, covering all the relevant topics and concepts.

3. Comprehensive Coverage: Exercise 1.4 includes a diverse range of problems and questions, providing students with practice in various aspects of sets.

4. Clear Explanations: Each class 11 ex 1.4 solution is explained in a clear and concise manner, helping students comprehend the underlying concepts and problem-solving techniques.
5. Preparation for Exams: These 11th class maths exercise 1.4 answers are a valuable resource for students preparing for their exams, as they offer ample practice to enhance their problem-solving skills and confidence.
6. Online Availability: NCERT Solutions for Class 11 Maths are often accessible online in various formats, including PDFs, making them convenient for a wide range of students.

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### Frequently Asked Question (FAQs)

1. What is union of sets ?

The union of set A and set B is a set that contains all the elements from set A as well as all the elements from set B.

2. What is intersection of sets ?

The intersection of set A and set B is a set that contains the common elements from set A  and set B.

3. If A = { 1,2,4,6} and B={2,1,6,7} than find the union of set A and B ?

A = { 1,2,4,6}

B={2,1,6,7}

A U B = { 1,2,4,6,7}

4. If A = { 1,2,4,6} and B={2,1,6,7} than find the intersection of set A and B ?

A = { 1,2,4,6}

B={2,1,6,7}

A ∩ B = { 1,2,6}

5. If A = { 1,2,4,6} and B={2,1,6,7} than find A - B ?

A = { 1,2,4,6}

B={2,1,6,7}

A - B = { 4}

6. If A = { 1,2,4,6} and B={2,1,6,7} than find B - A ?

A = { 1,2,4,6}

B={2,1,6,7}

B - A = { 7 }

7. If U is represent the union of set than U ∩ A ?

U ∩ A = A

8. Does A U B and B U A are same ?

Yes, A ∪ B = B ∪ A (Commutative law)

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