NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3) Exercise 1.3

NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3) Exercise 1.3

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NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3) Exercise 1.3 part-1

Access NCERT solutions for Math Chapter 1 – Sets Exercise 1.3

Exercise (1.3)

1. Make correct statements by filling in the symbols $\subset $ or $\not\subset $ in the blank spaces.

i. $\left\{ 2,3,4 \right\}...\left\{ 1,2,3,4,5 \right\}$

Ans:

Given that,

{2,3,4}...(1,2,3,4,5}
To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ 2,3,4 \right\}$ is also in the set $\left\{ 1,2,3,4,5 \right\}$

$\therefore \left\{ 2,3,4 \right\}\subset \left\{ 1,2,3,4,5 \right\}$


ii. $\left\{ a,b,c \right\}...\left\{ b,c,d \right\}$

Ans:

Given that,

$\left\{ a,b,c \right\}...\left\{ b,c,d \right\}$
To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ a,b,c \right\}$ is not in the set $\left\{ b,c,d \right\}$

$\therefore \left\{ a,b,c \right\}\not\subset \left\{ b,c,d \right\}$


iii. $\left\{ x:x\text{ is a student of class XI of your school} \right\}...$

$\left\{ x:x\text{ is a student of your school} \right\}$

Ans:

Given that,

$\left\{ x:x\text{ is a student of class XI of your school} \right\}...$

$\left\{ x:x\text{ is a student of your school} \right\}$
To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The set of students of class XI would also be inside the set of students in school

$\backepsilon  \left\{ x:x\text{ is a student of class XI of your school} \right\}\subset $$\left\{ x:x\text{ is a student of your school} \right\}$


iv. $\left\{ x:x\text{ is a circle in the plane } \right\}...$

$\left\{ x:x\text{ is a circle in the same plane with radius 1 unit} \right\}$

Ans:

Given that,

$\left\{ x:x\text{ is a circle in the plane } \right\}...$

$\left\{ x:x\text{ is a circle in the same plane with radius 1 unit} \right\}$
To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The set of circles in the plane with a unit radius will be in the set of the circles in the same plane. So the set of circles in the plane is not in the set of circles with unit radius in the same plane.

$\therefore \left\{ x:x\text{ is a circle in the plane } \right\}\not\subset $$\left\{ x:x\text{ is a circle in the same plane with radius 1 unit} \right\}$


v. $\left\{ x:x\text{ is a triangle in the plane} \right\}...$

$\left\{ x:x\text{ is a rectangle in the plane} \right\}$

Ans:

Given that,

$\left\{ x:x\text{ is a triangle in the plane} \right\}...$

$\left\{ x:x\text{ is a rectangle in the plane} \right\}$

To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the given expression itself, we know that the set of triangles in the plane are not in the set of rectangles in the plane.

$\therefore \left\{ x:x\text{ is a triangle in the plane} \right\}\not\subset $$\left\{ x:x\text{ is a rectangle in the plane} \right\}$


vi. $\left\{ x:x\text{ is an equilateral triangle in the plane} \right\}...$

$\left\{ x:x\text{ is a triangle in the plane} \right\}$

Ans:

Given that,

$\left\{ x:x\text{ is an equilateral triangle in the plane} \right\}...$$\left\{ x:x\text{ is a triangle in the plane} \right\}$

To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above expression, we know that the set of equilateral triangles in the plane is in the set of triangles in the same plane

$\therefore \left\{ x:x\text{ is an equilateral triangle in the plane} \right\}\subset $$\left\{ x:x\text{ is a triangle in the plane} \right\}$


vii. $\left\{ x:x\text{ is an even natural number} \right\}...\left\{ x:x\text{ is an integer} \right\}$

Ans:

Given that,

$\left\{ x:x\text{ is an even natural number} \right\}...\left\{ x:x\text{ is an integer} \right\}$
To fill in the correct symbols $\subset $ or $\not\subset $ inn the blank spaces

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The set of even natural numbers are in the set of integers.

$\therefore \left\{ x:x\text{ is an even natural number} \right\}\subset \left\{ x:x\text{ is an integer} \right\}$


2. Examine whether the following statements are true or false

i. $\left\{ a,b \right\}\not\subset \left\{ b,c,a \right\}$

Ans:

Given that,

$\left\{ a,b \right\}\not\subset \left\{ b,c,a \right\}$
To examine whether the above statement is true or false

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ a,b \right\}$ is also in the set $\left\{ b,c,a \right\}$

$\therefore \left\{ a,b \right\}\subset \left\{ b,c,a \right\}$

$\therefore $The given statement is false


ii. $\left\{ a,e \right\}\subset \left\{ x:x\text{ is an vowel in English alpahbet} \right\}$

Ans:

Given that,

$\left\{ a,e \right\}\subset \left\{ x:x\text{ is an vowel in English alpahbet} \right\}$

To examine whether the above statement is true or false

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ a,e \right\}$ is also in the set $\left\{ a,e,i,o,u \right\}$

$\therefore \left\{ a,e \right\}\subset \left\{ x:x\text{ is an vowel in English alpahbet} \right\}$

$\therefore $The given statement is true.


iii. $\left\{ 1,2,3 \right\}\subset \left\{ 1,3,5 \right\}$

Ans:

Given that,

$\left\{ 1,2,3 \right\}\subset \left\{ 1,3,5 \right\}$
To examine whether the above statement is true or false

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ 1,2,3 \right\}$ is not in the set $\left\{ 1,3,5 \right\}$ since $2\in \left\{ 1,2,3 \right\}$ and $2\notin \left\{ 1,3,5 \right\}$

$\left\{ 1,2,3 \right\}\not\subset \left\{ 1,3,5 \right\}$

$\therefore $The given statement is false.


iv. $\left\{ a \right\}\subset \left\{ a,b,c \right\}$

Ans:

Given that,

$\left\{ a \right\}\subset \left\{ a,b,c \right\}$

To examine whether the above statement is true or false

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ a \right\}$ is also in the set $\left\{ a,b,c \right\}$

$\therefore \left\{ a \right\}\subset \left\{ a,b,c \right\}$

$\therefore $The given statement is true.


v. $\left\{ a \right\}\in \left\{ a,b,c \right\}$

Ans:

Given that,

$\left\{ a \right\}\in \left\{ a,b,c \right\}$
To examine whether the above statement is true or false

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

The element in the set $\left\{ a \right\}$ and the elements in the set $\left\{ a,b,c \right\}$ are $a,b,c$

$\therefore \left\{ a \right\}\subset \left\{ a,b,c \right\}$

$\therefore $The given statement is false.


vi. $\left\{ x:x\text{ is an even natural less than 6} \right\}\subset $$\left\{ x:x\text{ is a natural number which divide 36} \right\}$

Ans:

Given that,

$\left\{ x:x\text{ is an even natural less than 6} \right\}\subset $$\left\{ x:x\text{ is a natural number which divide 36} \right\}$To examine whether the above statement is true or false

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

$\left\{ x:x\text{ is an even natural less than 6} \right\}=\left\{ 2,4 \right\}$

$\left\{ x:x\text{ is a natural number which divide 36} \right\}=\left\{ 1,2,3,4,6,9,12,18,36 \right\}$$\therefore \left\{ x:x\text{ is an even natural less than 6} \right\}\subset $$\left\{ x:x\text{ is a natural number which divide 36} \right\}$

$\therefore $The given statement is true.


3. Let $A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$. Which of the following statements are incorrect and why?

i. $\left\{ 3,4 \right\}\subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ 3,4 \right\}\subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

$3\in \left\{ 3,4 \right\}$, however $3\notin A$

$\therefore $The given statement $\left\{ 3,4 \right\}\subset A$ is incorrect


ii. $\left\{ 3,4 \right\}\in A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ 3,4 \right\}\in A$ is correct or incorrect.

From the above statement,

$\left\{ 3,4 \right\}$ is an element of A.

$\therefore \left\{ 3,4 \right\}\in A$

$\therefore $The given statement is correct.


iii. $\left\{ \left\{ 3,4 \right\} \right\}\subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ \left\{ 3,4 \right\} \right\}\subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

$\left\{ 3,4 \right\}\in \left\{ \left\{ 3,4 \right\} \right\}$ so that $\left\{ \left\{ 3,4 \right\} \right\}\in A$

$\therefore \left\{ \left\{ 3,4 \right\} \right\}\subset A$

$\therefore $The given statement $\left\{ \left\{ 3,4 \right\} \right\}\subset A$ is correct.


iv. $1\in A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $1\in A$ is correct or incorrect.

From the above statement,

$1$ is an element of A.

$\therefore $The statement $1\in A$ is a correct statement.


v. $1\subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $1\subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

An element of a set can never be a subset of itself. So $1\not\subset A$

$\therefore $The given statement $1\subset A$ is an incorrect statement.


vi. $\left\{ 1,2,5 \right\}\subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ 1,2,5 \right\}\subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

The each element of $\left\{ 1,2,5 \right\}$ is also an element of A, So $\left\{ 1,2,5 \right\}\subset A$

$\therefore $The given statement $\left\{ 1,2,5 \right\}\subset A$ is a correct statement 


vii. $\left\{ 1,2,5 \right\}\in A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ 1,2,5 \right\}\subset A$ is correct or incorrect.

From the above statement,

Element of $\left\{ 1,2,5 \right\}$ is not an element of A, So $\left\{ 1,2,5 \right\}\notin A$

So the given statement $\left\{ 1,2,5 \right\}\in A$ is an incorrect statement.


viii. $\left\{ 1,2,3 \right\}\subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ 1,2,3 \right\}\subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement, we notice that,

$3\in \left\{ 1,2,3 \right\}$but $3\notin A$

$\left\{ 1,2,3 \right\}\not\subset A$

$\therefore $The given statement $\left\{ 1,2,3 \right\}\subset A$ is an incorrect statement.


ix. $\varnothing \in A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\varnothing \in A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

$\varnothing $ is not an element of A. So, $\varnothing \notin A$

$\therefore $The given statement $\varnothing \in A$ is an incorrect statement.


x. $\varnothing \subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\varnothing \subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

Since $\varnothing $  is a subset of every set, $\varnothing \subset A$

$\therefore $The given statement $\varnothing \subset A$ is a correct statement.


xii. $\left\{ \varnothing  \right\}\subset A$

Ans:

Given that,

$A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$

To find if $\left\{ \varnothing  \right\}\subset A$ is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

From the above statement,

$\varnothing $ is an element of A and it is not a subset of A. 

$\therefore $The given statement $\left\{ \varnothing  \right\}\subset A$ is an incorrect statement.


4. Write down all the subsets of the following sets:

i. $\left\{ a \right\}$

Ans:

Given that,

$\left\{ a \right\}$

To write the subset of the given sets

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

Subsets of $\left\{ a \right\}$ are $\varnothing $ and $\left\{ a \right\}$


ii. $\left\{ a,b \right\}$

Ans:

Given that,

$\left\{ a,b \right\}$

To write the subset of the given sets

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

Subsets of $\left\{ a,b \right\}$ are $\varnothing $ and $\left\{ a \right\},\left\{ b \right\},\left\{ a,b \right\}$


iii. $\left\{ 1,2,3 \right\}$

Ans:

Given that,

$\left\{ 1,2,3 \right\}$

To write the subset of the given sets

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

Subsets of $\left\{ 1,2,3 \right\}$ are $\varnothing $,$\left\{ 1 \right\},\left\{ 2 \right\},\left\{ 3 \right\},\left\{ 1,2 \right\},\left\{ 2,3 \right\},\left\{ 1,3 \right\},\left\{ 1,2,3 \right\}$


iv. $\varnothing $

Ans:

Given that,

$\varnothing $

To write the subset of the given sets

A set A is said to be a subset of B if every element of A is also an element of B

$A\subset B$ if $a\in A,a\in B$

Subsets of $\varnothing $ is $\varnothing $.


5. How many elements has $P\left( A \right)$, if $A=\varnothing $?

Ans:

Given that,

$A=\varnothing $

To find the number of elements does the $P\left( A \right)$ contain

The collection of all subsets of a set A is called a power set of A and is denoted by $P\left( A \right)$.

We know that if $A$ is a set with $m$elements, that is, $n\left( A \right)=m$, then $n\left[ p\left( A \right) \right]={{2}^{m}}$

If $A=\varnothing $ then $n\left( A \right)=0$

$n\left[ P\left( A \right) \right]={{2}^{0}}$

$=1$

$\therefore P\left( A \right)$ has only one element.


6. Write the following as intervals

i. $\left\{ x:x\in R,-4<x\le 6 \right\}$

Ans:

Given that,

$\left\{ x:x\in R,-4<x\le 6 \right\}$

To write the above expression as intervals

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore \left\{ x:x\in R,-4<x\le 6 \right\}=(-4,6]$


ii. $\left\{ x:x\in R,-12<x<-10 \right\}$

Ans:

Given that,

$\left\{ x:x\in R,-12<x<-10 \right\}$

To write the above expression as intervals

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore \left\{ x:x\in R,-12<x<-10 \right\}=\left( -12,-10 \right)$


iii. $\left\{ x:x\in R,0\le x<7 \right\}$

Ans:

Given that,

$\left\{ x:x\in R,0\le x<7 \right\}$

To write the above expression as intervals

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\because \left\{ x:x\in R,0\le x<7 \right\}=[0,7)$


iv. $\left\{ x:x\in R,3\le x\le 4 \right\}$

Ans:

Given that,

$\left\{ x:x\in R,3\le x\le 4 \right\}$

To write the above expression as intervals

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore \left\{ x:x\in R,3\le x\le 4 \right\}=\left[ 3,4 \right]$


7. Write the following intervals in set builder form.

i. $\left( -3,0 \right)$

Ans:

Given that,

$\left( -3,0 \right)$

To write the above interval in set builder form

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore \left( -3,0 \right)=\left\{ x:x\in R,-3<x<0 \right\}$


ii. $\left[ 6,12 \right]$

Ans:

Given that,

$\left[ 6,12 \right]$

To write the above interval in set builder form

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore \left[ 6,12 \right]=\left\{ x:x\in R,6\le x\le 12 \right\}$


iii. $(6,12]$

Ans:

Given that,

$(6,12]$

To write the above interval in set builder form

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore (6,12]=\left\{ x:x\in R,6<x\le 12 \right\}$


iv. $[-23,5)$

Ans:

Given that,

$[-23,5)$

To write the above interval in set builder form

The set of real numbers $\left\{ y:a<y<b \right\}$ is called an open interval and is denoted by $\left( a,b \right)$. The interval which contains the end points also is called close interval and is denoted by$\left[ a,b \right]$

$\therefore [-23,5)=\left\{ x:x\in R,-23\le x<5 \right\}$


8. What universal set(s) would you propose for each of the following:

i. The set of right triangles

Ans:

To propose the universal set for the set of right triangles

For the set of right triangles, the universal set can be the set of all kinds of triangles or the set of polygons.


ii. The set of isosceles triangles

Ans:

To propose the universal set for the set of right triangles

For the set of isosceles triangles, the universal set can be the set of all kinds of triangles or the set of polygons or the set of two dimensional figures.


9. Given the sets $A=\left\{ 1,3,5 \right\},B=\left\{ 2,4,6 \right\}$ and $C=\left\{ 0,2,4,6,8 \right\}$, which of the following may be considered as universal set(s) for all the three sets A, B and C?

i. $\left\{ 0,1,2,3,4,5,6 \right\}$

Ans:

Given that,

$A=\left\{ 1,3,5 \right\},B=\left\{ 2,4,6 \right\},C=\left\{ 0,2,4,6,8 \right\}$

To find if the given set $\left\{ 0,1,2,3,4,5,6 \right\}$ is the universal set of A, B and C

It can be observed that,

$A\subset $$\left\{ 0,1,2,3,4,5,6 \right\}$

$B\subset $$\left\{ 0,1,2,3,4,5,6 \right\}$

$C\not\subset $$\left\{ 0,1,2,3,4,5,6 \right\}$

$\therefore $The set $\left\{ 0,1,2,3,4,5,6 \right\}$ cannot be the universal set for the sets A, B and C


ii. $\varnothing $

Ans:

Given that,

$A=\left\{ 1,3,5 \right\},B=\left\{ 2,4,6 \right\},C=\left\{ 0,2,4,6,8 \right\}$

To find if the given set $\varnothing $ is the universal set of A, B and C

It can be observed that,

$A\not\subset \varnothing $

$B\not\subset \varnothing $

$C\not\subset \varnothing $

$\therefore $The set $\varnothing $ cannot be an universal set for A, B and C.


iii. $\left\{ 0,1,2,3,4,5,6,7,8,9,10 \right\}$

Ans:

Given that,

$A=\left\{ 1,3,5 \right\},B=\left\{ 2,4,6 \right\},C=\left\{ 0,2,4,6,8 \right\}$

To find if the given set $\left\{ 0,1,2,3,4,5,6,7,8,9,10 \right\}$ is the universal set of A, B and C

It can be observe that,

$A\subset $$\left\{ 0,1,2,3,4,5,6,7,8,9,10 \right\}$

$B\subset $$\left\{ 0,1,2,3,4,5,6,7,8,9,10 \right\}$

$C\subset $$\left\{ 0,1,2,3,4,5,6,7,8,9,10 \right\}$

$\therefore $The set $\left\{ 0,1,2,3,4,5,6,7,8,9,10 \right\}$ is the universal set of A, B and C


iv. $\left\{ 1,2,3,4,5,6,7,8 \right\}$

Ans:

Given that,

$A=\left\{ 1,3,5 \right\},B=\left\{ 2,4,6 \right\},C=\left\{ 0,2,4,6,8 \right\}$

To find if the given set $\left\{ 0,1,2,3,4,5,6 \right\}$ is the universal set of A, B and C

It can be observed that,

$A\subset $$\left\{ 1,2,3,4,5,6,7,8 \right\}$

$B\subset $$\left\{ 1,2,3,4,5,6,7,8 \right\}$

$C\not\subset $$\left\{ 1,2,3,4,5,6,7,8 \right\}$

$\therefore $The set $\left\{ 1,2,3,4,5,6,7,8 \right\}$ is not the universal set of A, B and C


NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3) Exercise 1.3

The NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3 deals with a variety of essential concepts such as Subsets, Power Sets, Universal Sets, Venn Diagrams, and Operation of Sets. Vedantu’s Exercise 1.3 class 11 maths solutions include all requisite examples and formulas and answers you need to study. They have been devised to not only make you familiar with the subject but also help you easily grasp complex concepts. Class 11 Maths NCERT Solutions Chapter 1 will come in handy while preparing for your exams. They help you become thorough with the subject so that you can attain the desired score in your exams. They make learning more fun, intriguing, and useful.

A subject like maths can be quite daunting and intimidating, especially when you are in class 11 or 12. Vedantu’s carefully designed Class 11 Maths NCERT Solutions Chapter 1 will guide you step by step. They have been designed to help you understand how to answer each question type from this chapter. The Class 11 Maths Exercise 1.3 Solution will help you practice your way to perfection. With Vedantu as your study buddy, Class 11 Exercise 1.3 will not give you sleepless nights.

At the end of every chapter, you will find extensive exercises and solved examples. You will also find a shortlist and summary of essential concepts learned in the chapter at the end of each chapter that can be used for quick revision reference right before your exams.

Here is why you should hang on to Vedantu’s Ex.1.3 Class 11 Solutions.

  • Vedantu’s NCERT solutions are all-inclusive and highly organized.

  • They are easy to understand and remember.

  • 11th Maths Exercise 1.3 Answers have been prepared according to CBSE Board and NCERT guidelines.

  • NCERT Solution for Class 11 Maths Chapter 1 Exercise 1.3 has been devised by expert teachers based on established study strategies that help in maximum retention and the highest level of conceptual understanding. They are of excellent quality and 

  • Vedantu’s NCERT Solutions are comprehensive, exhaustive, yet precise. They are complete set of solutions of Exercise 1.3 which helps in time and effort saving.

  • With Vedantu on your side, you can learn anywhere anytime. You have the option to download a free PDF version of Ex. 1.3 Class 11 Maths NCERT solutions. You can choose to study online or offline based on your requirements.

  • Exercise 1.3 Class 11 Maths comprehensive solutions are 100 per cent accurate. They help you pass your exams with flying colours.


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FAQs (Frequently Asked Questions)

Q1. On which platform can I find NCERT Solutions for Class 11 Maths Chapter 1 Sets EX 1.3?

Ans: Students can find exercise-wise NCERT Solutions for Class 11 Maths Chapter 1 Sets on Vedantu. Vedantu is a reliable platform to avail NCERT Solutions. NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.3 is available in a free to download PDF format. Students can avail these solutions provided by expert tutors at Vedantu. In case of any doubts in solving the exercise or other exercises of the chapter Sets, students can refer to Vedantu’s site for the needed solutions.

Q2. Why must One Consider Vedantu’s NCERT Solutions for Class 11 Maths Chapter 1 Sets for Ex 1.3 and Other Exercises?

Ans: The exercise-wise NCERT Solutions for Class 11 Maths Chapter 1 Sets by Vedantu are the most comprehensive and well-designed exam material. It can be easily accessed over the internet without any paid subscription. The solutions are available in the downloadable PDF so that students can study offline as well. NCERT Solutions for Class 11 Mathematics Chapter 1 Sets include step-by-step explanations by the expert and experienced tutors. It helps students in practising the chapter in a better manner.

Q3. Define Sets and Give Examples.

Ans:  A set is a well-defined group or collection of objects or numbers. Each object or number which is a part of a set is called the elements or members of a set. Examples include a set of rational numbers, a set of types of fruits, a set of English alphabets, etc.

Q4. What is the difference between the Finite and Infinite Set?

Ans: Given below is the difference between the finite and infinite set:

Finite Set: 

A set consisting of a finite or countable number of elements is called a Finite Set. 

Examples:

  1. A set of all English alphabets. 

  2. Q = { a : a is an integer, 1 < a < 20}

Infinite Set: 

A set consisting of an infinite number of elements is called an Infinite Set. 

Examples:

  1. A set of all points on a line

  2. The set of all integers

Q5. What is the best Solution book for NCERT Class 11 Maths?

Ans: Students can access the NCERT Solutions for free on the Vedantu website (vedantu.com) or app. Download a PDF version of the NCERT Class 11 Maths Solutions from the page NCERT Solutions for Class 11 Maths. Students can also access other study material like revision notes, important questions, and formulas related to this chapter from the app or website (vedantu.com) free of cost. To ace your tests, you must put in a lot of practice.

Q6. How many chapters are there in NCERT Class 11 Maths?

Ans: The NCERT Class 11 Maths textbook has 16 chapters as well as some random problems for each topic. Each chapter must be given equal weight to have a comprehensive grasp of all of the topics provided for Class 11 students and perform well in your examinations. If you try to skip a chapter, your understanding will suffer. You may simply get extra help by visiting the link NCERT Solutions for Class 11 Maths on Vedantu website(vednatu.com) or app.

Q7. What are the challenging chapters in Class 11 Maths?

Ans: Even though each chapter has questions and relevance for an overall grasp of ideas across multiple areas of Maths, students often struggle while studying trigonometry, binomial theorem, and limits and derivatives. Prepare well for these chapters by practising NCERT questions, as well as all of the previous chapters. Difficulty levels also differ from one pupil to the next. Solve multiple problems, and you can check the solutions of NCERT problems from the link NCERT Solutions for Class 11 Maths of Vedantu website (vedantu.com).

Q8. What are sets in Class 11 Maths?

Ans: A set is any collection of objects (elements) that may or may not be Mathematical in Mathematics and logic (e.g., numbers, functions). For example, the set of integers from 1 to 50 is finite, but the set of all integers is infinite. A set is typically expressed as a list of all its members wrapped in braces. Practice different problems as well for a better understanding.

Q9. Why study Sets in Class 11 Maths?

Ans: Sets are used to store a collection of linked items. They are significant in all fields of Mathematics because sets are used or referred to in some manner in every discipline of Mathematics. They are necessary for the construction of increasingly sophisticated Mathematical structures. Moreover, it is very crucial to learn the fundamentals properly before advancing to more complex topics.

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