NCERT Solutions for Class 11 Maths Chapter 1 Sets
Free PDF download of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.4 (Ex 1.4) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 11 Maths Chapter 1 Sets Exercise 1.4 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register and get all exercise solutions in your emails.
Class:  
Subject:  
Chapter Name:  
Exercise:  Exercise  1.4 
ContentType:  Text, Videos, Images and PDF Format 
Academic Year:  202425 
Medium:  English and Hindi 
Available Materials: 

Other Materials 

Access NCERT Solutions for Mathematics Chapter 1 – Sets
Exercise 1.4
1. Find the union of each of the following pairs of sets.
(i)\[{\mathbf{x}} = \{ {\mathbf{1}},{\mathbf{3}},{\mathbf{5}}\} {\text{ }}{\mathbf{Y}} = \{ {\mathbf{1}},{\mathbf{2}},{\mathbf{3}}\} \]
Ans: $X = \{ 1,3,5\} Y = \{ 1,2,3\} $
$X \cup Y = \{ 1,2,3,5\} $
(ii) \[{\mathbf{A}} = {\text{ }}\left\{ {{\mathbf{a}},{\text{ }}{\mathbf{e}},{\text{ }}{\mathbf{i}},{\text{ }}{\mathbf{o}},{\text{ }}{\mathbf{u}}} \right\}{\text{ }}{\mathbf{B}} = {\text{ }}\left\{ {{\mathbf{a}},{\text{ }}{\mathbf{b}},{\text{ }}{\mathbf{c}}} \right\}\]
Ans: $A = \{ a,e,i,o,u\} B = \{ a,b,c\} $
$A \cup B = \{ a,b,c,e,i,o,u\} $
(iii) A= {x. x is a natural number and multiple of 3$\} $
Ans: $A = \{ x:x$ is a natural number and multiple of 3$\} = \{ 3,6,9 \ldots \} $
As $B = \{ x:x$ is a natural number less than 6$\} = \{ 1,2,3,4,5,6\} $
$A \cup B = \{ 1,2,4,5,3,6,9,12 \ldots \} $
$\therefore A \cup B = \{ x:x = 1,2,4,5$ or a multiple of 3$\} $
(iv) A= {x : x is a natural number and $1 < x \leqslant 6\} = \{ 2,3,4,5,6\} $
$B = \{ x:x$ is a natural number and $6 < x < 10\} = \{ 7,8,9\} $
Ans: $A \cup B = \{ 2,3,4,5,6,7,8,9\} $
$\therefore A \cup B = \{ x:x \in N$ and $1 < x < 10\} $
(v) $A = \{ 1,2,3\} ,B = \phi $
Ans: $A = \{ 1,2,3\} ,B = \phi $
$A \cup B = \{ 1,2,3\} $
2. Let $A = \{ a,b\} ,B = \{ a,b,c\} .$ Is $A \subset B?$ What is $A \cup B$ ?
Ans: Here, $A = \{ a,b\} $ and $B = \{ a,b,c\} $
Yes, $A \subset B$
$A \cup B = \{ a,b,c\} = B$
3. If A and B are two sets such that $A \subset B$, then what is $A \cup B$?
Ans: If ${\text{A}}$ and ${\text{B}}$ are two sets such that $A \subset B$, then $A \cup B = B$.
4. If $A = \{ 1,2,3,4\} ,B = \{ 3,4,5,6\} ,C = \{ 5,6,7,8\} $ and $D = \{ 7,8,9,10\} ;$ find
(i) $A \cup B$
Ans: $A \cup B = \{ 1,2,3,4,5,6\} $
(ii) $A \cup C$
Ans: $A \cup C = \{ 1,2,3,4,5,6,7,8\} $
(iii) $B \cup C$
Ans: $B \cup C = \{ 3,4,5,6,7,8\} $
(iv) $B \cup D$
Ans: $B \cup D = \{ 3,4,5,6,7,8,9,10\} $
(v) \[A \cup B \cup C\]
Ans: $A \cup B \cup C = \{ 1,2,3,4,5,6,7,8\} $
(vi) \[A \cup B \cup D\]
Ans: $A \cup B \cup D = \{ 1,2,3,4,5,6,7,8,9,10\} $
(vii) $B \cup C \cup D$
Ans: $B \cup C \cup D = \{ 3,4,5,6,7,8,9,10\} $
5. Find the intersection of each pair of sets.
(i) $X = \{ 1,3,5\} Y = \{ 1,2,3\} $
Ans: $X \cap Y = \{ 1,3\} $
(ii) $A = \{ a,e,i,o,u\} B = \{ a,b,c\} $
Ans: $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 \[{\mathbf{6}}\]$\} $
Ans: $\therefore A \cap B = \{ 3\} $
(iv) $A = \{ x:x$ is a natural number and $1 < x \leqslant 6\} $
$B = \{ x:x$ is a natural number and $6 < x < 10\} $
Ans: $A = \{ x:x$ is a natural number and $1 < x \leqslant 6\} = \{ 2,3,4,5,6\} $
$B = \{ x:x$ is a natural number and $6 < x < 10\} = \{ 7,8,9\} $
$A \cap B = \emptyset $
(v) $A = \{ 1,2,3\} ,B = \emptyset $
Ans: $A \cap B = \emptyset $
6. If $A = \{ 3,5,7,9,11\} ,B = \{ 7,9,11,13\} ,C = \{ 11,13,15\} $ and $D = \{ 15,17\} ;$ find
(i) $A \cap B$
Ans: $A \cap B = \{ 7,9,11\} $
(ii) $B \cap C$
Ans: $B \cap C = \{ 11,13\} $
(iii) $A \cap C \cap D$
Ans: $A \cap C \cap D = \{ A \cap C\} \cap D = \{ 11\} \cap \{ 15,17\} = \emptyset $
(iv) $A \cap C$
Ans: $A \cap C\{ 11\} $
(v) $B \cap D$
Ans: $B \cap D = \emptyset $
(vi) $A \cap (B \cup C)$
Ans: $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
$ = \{ 7,9,11\} \cup \{ 11\} = \{ 7,9,11\} $
(vii) $A \cap D$
Ans: $A \cap D = \emptyset $
(viii) $A \cap (B \cup D)$
Ans: $A \cap (B \cup D) = (A \cap B) \cup (A \cap D)$
$ = \{ 7,9,11\} \cup \emptyset = \{ 7,9,11\} $
(ix) $(A \cap B) \cap (B \cup C)$
Ans: $(A \cap B) \cap (B \cup C) = \{ 7,9,11\} \cap \{ 7,9,11,13,15\} = \{ 7,9,11\} $
(x) $(A \cup D) \cap (B \cup C)$
Ans: $(A \cup D) \cap (B \cup C) = \{ 3,5,7,9,11,15,17\} \cap \{ 7,9,11,13,15\} $
$ = \{ 7,9,11,15\} $
7. If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number}
$C = \{ x:x$ is an odd natural number} and $D = \{ x:x$ is a prime number}, find
$A = \{ x:x$ is a natural number $\} = \{ 1,2,3,4,5 \ldots \} $
$B = \{ x:x$ is an even natural number $\} = \{ 2,4,6,8 \ldots \} $
$C = \{ x:x$ is an odd natural number $\} = \{ 1,3,5,7,9 \ldots \} $
$D = \{ x:x$ is a prime number $\} = \{ 2,3,5,7 \ldots \} $
(i) $A \cap B$
Ans: $A \cap B = \{ x:x$ is an even natural number $\} = B$
(ii) $A \cap C$
Ans: $A \cap C = \{ x:x$ is an odd natural number $\} = C$
(iii) $A \cap D$
Ans: $A \cap D = \{ x:x$ is a prime number $\} = D$
(iv) $B \cap C$
Ans: $B \cap C = \emptyset $
(v) $B \cap D$
Ans: $B \cap D = \{ 2\} $
(vi) $C \cap D$
Ans: $C \cap D = \{ x:x$ is odd prime number $\} $
8. Which of the following pairs of sets are disjoint
(i) $\{ 1,2,3,4\} $ and $\{ x:x$ is a natural number and \[4 \leqslant x \leqslant 6\} \]
Ans: $\{ 1,2,3,4\} $
$\{ x:x$ is a natural number and $4 \leqslant x \leqslant 6\} = \{ 4,5,6\} $
Now, $\{ 1,2,3,4\} \cap \{ 4,5,6\} = \{ 4\} $
Therefore, this pair of sets is not disjoint.
(ii) {a,e,I,o,u} and {c,d,e,f}
Ans: $\{ a,e,i,o,u\} \cap \{ c,d,e,f\} = \{ e\} $
Therefore, $\{ a,e,i,o,u\} $ and $\{ c,d,e,f\} $ are not disjoint.
(iii) $\{ x:x$ is an even integer} and $\{ x:x$ is an odd integer}
Ans: $\{ x:x$ is an even integer $\} \cap \{ x:x$ is an odd integer $\} = \emptyset $
Therefore, this pair of sets is disjoint.
9. If $A = \{ 3,6,9,12,15,18,21\} ,B = \{ 4,8,12,16,20\} $,
$C = \{ 2,4,6,8,10,12,14,16\} ,D = \{ 5,10,15,20\} ;$ find
(i) AB
Ans: $A  B = \{ 3,6,9,15,18,21\} $
(ii) AC
Ans: $A  C = \{ 3,9,15,18,21\} $
(iii) AD
Ans: $A  D = \{ 3,6,9,12,18,21\} $
(iv) BA
Ans: $B  A = \{ 4,8,16,20\} $
(v) CA
Ans: $C  A = \{ 2,4,8,10,14,16\} $
(vi) DA
Ans:$D  A = \{ 5,10,20\} $
(viii) BC
Ans: $B  C = \{ 20\} $
(viii) BD
Ans: $B  D = \{ 4,8,12,16\} $
(ix) CB
Ans: $C  B = \{ 2,6,10,14\} $
(x) DB
Ans: $D  B = \{ 5,10,15\} $
(xi) CD
Ans: $C  D = \{ 2,4,6,8,12,14,16\} $
(xii) DC
Ans: $D  C = \{ 5,15,20\} $
10. If $X = \{ a,b,c,d\} $ and $Y = \{ f,b,d,g\} $, find
(i) XY
Ans: $X  Y = \{ a,c\} $
(ii) YX
Ans: $Y  X = \{ f,g\} $
(iii) $X \cap Y$
Ans:$X \cap Y = \{ b,d\} $
11. If R is the set real numbers and Q is the set of rational numbers, then what is RQ?
Ans: R. Set of real numbers
Q. Set of rational numbers
Therefore, ${\text{R}}  {\text{Q}}$ is a set of irrational number.
12. State whether each of the following statement is true or false. Justify you Ans:
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
Ans: False
As $3 \in \{ 2,3,4,5\} ,3 \in \{ 3,6\} $
$ \Rightarrow \{ 2,3,4,5\} \cap \{ 3,6\} = \{ 3\} $
(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.
Ans: False
As $a \in \{ a,e,i,o,u\} ,a \in \{ a,b,c,d\} $
$ \Rightarrow \{ a,e,i,o,u\} \cap \{ a,b,c,d\} = \{ a\} $
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
Ans: True
As $\{ 2,6,10,14\} \cap \{ 3,7,11,15\} = \emptyset $.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
Ans: True
As $\{ 2,6,10\} \cap \{ 3,7,11\} = \emptyset $
NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4
Opting for the NCERT solutions for Ex 1.4 Class 11 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 1.4 Class 11 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
Vedantu inhouse subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 11 students who are thorough with all the concepts from the Maths textbook and quite wellversed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 11 Maths Chapter 1 Exercise 1.4 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.
Besides these NCERT solutions for Class 11 Maths Chapter 1 Exercise 1.4, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our inhouse subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.
Do not delay any more. Download the NCERT solutions for Class 11 Maths Chapter 1 Exercise 1.4 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.
NCERT Solution Class 11 Maths of Chapter 1 All Exercises
Exercises  Number of Questions 
6 Questions & Solutions  
6 Questions & Solutions  
9 Questions & Solutions  
7 Questions & Solutions  
9 Questions & Solutions 
CBSE Class 11 Maths Chapter 11 Other Study Materials
NCERT Class 11 Maths Solutions Chapterwise Links  Download the FREE PDF
S. No  NCERT Solutions Class 11 Maths All Chapters 
1  
2  
3  
4  Chapter 4  Complex Numbers and Quadratic Equations Solutions 
5  
6  
7  
8  
9  
10  
11  Chapter 11  Introduction to Three Dimensional Geometry Solutions 
12  
13  
14 
Important Related Links for CBSE Class 11 Maths
S. No  Important Study Material for CBSE Class 11 Maths 
1  
2  
3  
4  
5 