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Edited By Ravindra Pindel | Updated on Sep 12, 2022 04:38 PM IST

**NCERT Exemplar Class 11 Maths solutions chapter 1** Sets deals with a variety of definitions and terms related to a set which was first introduced by Georg Cantor which serves a very important part at each, and every branch of mathematics in present times. The chapter has its reach in various different topics such as geometry, trigonometry, sequence, etc., which makes it even more vital to be understood. With the help of NCERT Exemplar Class 11 Maths chapter 1 solutions, students will be able to understand the application of sets. NCERT Exemplar solutions Class 11 Maths chapter 1 also helps in identifying whether a collection could be termed as a set or not. The essential rules like a set is denoted by a capital letter, its members or objects are represented by small letters, and the terms and objects of the collection should be synonymous, are also explained.

**JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | **

**Suggested: ****JEE Main: high scoring chapters | ****Past 10 year's papers**

This Story also Contains

- NCERT Exemplar Class 11 Maths Solutions Chapter 1: Short Answer Type
- NCERT Exemplar Class 11 Maths Solutions Chapter 1: Long Answer Type
- NCERT Exemplar Class 11 Maths Solutions Chapter 1: Objective Type
- Important Notes To Follow While Studying NCERT Exemplar Class 11 Maths Solutions Chapter 1 Sets
- Main Subtopics of NCERT Exemplar Class 11 Maths Solutions Chapter 1
- What will the students learn in NCERT Exemplar Class 11 Maths Solutions Chapter 1?
- NCERT Solutions for Class 11 Mathematics Chapters
- Important Topics To Cover in NCERT Exemplar Class 11 Maths Solutions Chapter 1 Sets

Question:

is a positive factor of a prime number

Answer:

(i) Given that

; Hence ,

(ii) Given that

, ; Hence

(iii) Given that is a positive factor of a prime number

So , the positive factors of prime number P are 1 and P . Hence ,

Question:

Write the following sets in the roaster form:

Answer:

(i) Given that ** ** ** ** ** ** ** **

(ii) Given that ** ** ** ** ** ** ** **

Hence ,

(iii) Given that ** ** ** ** ** ** ** ** ** **

Hence

Question:

Write the following sets in the roaster form:

Answer:

(i) Given that:

Hence,

(ii) Given that

Hence,

(iii) Given that

So the positive factors of prime number are 1 and . Hence

Question:

Write the following sets in the roaster form:

Answer:

(i) Given that

hence,

(ii) Given that

Hence,

(iii) Given that

and

Hence,

Question:

If . Write Y in the roaster form.

Answer:

Given that

The factors of are

The factors of are 1 and

Hence,

Question:

Answer:

(i) Given that:

Factors of 35 are 1, 5, 7, 35.

Hence, true

(ii) Given that:

Factors of 128 are 1,2,4,8,16,32,64,128

sum of all factors

hence statement is false.

(iii) Given that:

Put x = 3

which is not true, So 3 is not an element of the set

Hence, statement is true

(iv) Given that:

The positive factors of 496 are 1,2,4,8,16, 31, 62, 124, 248, and 496

The sum of all positive factors is which is true, so the 496 is element of the set . Hence the statement is false.

Question:

Answer:

(i) Given that and

To prove: we have to show that if

Let

hence,

(ii) then let

But

From (i) and (ii) we get

Now if , then

let

Hence,

Thus,

iii)

Question:

Answer:

N = {1,2,3,4……100}

Required subset whose elements are even = {2,4, 6,8…..,100}

Required subset whose elements are perfect squares = {1,4,9 ,16,25,36,49,64,81,100}

Question:

Answer:

Given that

(i)

(ii)

(iii)

(iv)

Question:

Answer:

Given that: Y = {1, 2, 3,…, 10}

(i)

(ii)

(iii)

Question:

Answer:

Given that: A, B and C are the subsets of a universal set U.

Where A= {2,4,6,8,12,20}

B = {3, 6,9, 12, 15}

And C = {5, 10, 15, 20}

Question:

Answer:

Given that U: Set of all boys and girls

G = Set of girls

B = Set of boys

S = Set of all students who take swimming

Question:

For all sets A, B and C, A – (B – C) = (A – B) – C

Answer:

Let us use the following Venn diagram to solve this question

Step 1: - B - C

Step 2: - A-(B-C)

Step 3: - A-B

Step 4: - (A-B)-C

As steps 2 and 4 are inequal, hence, the statement given is not true.

Question:

For all sets A, B and C, if A ⊂ B, then A ∩ C ⊂ B ∩ C

Answer:

Suppose ,

Let

Hence the given statement is true.

Question:

For all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C

Answer:

Suppose ,

Let

Hence the given statement is true.

Question:

For all sets A, B and C, if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C

Answer:

Suppose .

Let

hence the given statement is true

Question:

Let A, B and C be sets. Then show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Answer:

Let

Let

From and (i) and (ii)

Question:

Answer:

Let the set of students who passed in mathematics be M, the set of students who passed in English be E and set of students who passed in science be S.

Then n(U)=100, n(M)=12, n(S)=8,

and

According to the Venn diagram

Thus, number of students who passed in English and mathematics but not in science = d= 2

Number of students who passed in Science and mathematics but not in English = f=3

Number of students who passed in mathematics only = g =3

Number of students who passed in more than one subject = b+ e+ d +f =0+4+2+3 =9

Question:

Answer:

Let C be the set of students who play cricket and T the set of students who play tennis.

Total number of students = 60 ⇒n(U)=60

Number of students who play cricket = 25 n(C)=25

Number of students who play tennis = 20 n(T)=20

Number of students who play both the games = 10

Number of students who play any one game

Number of students who play neither

Question:

Answer:

Let A be a set of families which buy newspaper A, B be the set of families which buy newspaper B and C be the set of families which buy newspaper C

and

Number of families which buy newspaper A only

Number of families which buy none of A, B and C

Question:

Answer:

Let the set of students who study mathematics be M, the set of students who study physics be P and set of students who study chemistry be C.

N(U) =200, n(M)=120, n(P)=90, n(C)=70, n(MP) = 40, , and

Hence, the number of students who study all 3 subjects = 20

Question:

Answer:

Let F be the set of students who study French, E be the set of students who study English and S be the set of students who study Sanskrit

and

Number of students who study French only =a =6

Number of students who study English only =c =3

Number of students who study Sanskrit only =g =9

Number of students who study English and Sanskrit but not French =f =1

Number of students who study French and Sanskrit but not English =d =2

Number of students who study French and English but not Sanskrit =b = 6

Number of students who study at least one of the three languages = a+b+c+d+e+f+g =6+6+3+2+3+1+9 =30

Number of students who study none of the three languages = 50-30=20

Question:

Answer:

Number of elements in

However, each element is repeated 10 times.

Number of elements in

But each element is repeated 09 times

From (i) and (ii) we get . hence, the correct option is (c)

Question:

According to the question we have,

Question:

The set (A ∩ B′)′ ∪ (B ∩ C) is equal to

A. A′∪ B ∪ C

B. A′ ∪ B

C. A′ ∪ C′

D. A′ ∩ B

Answer:

The answer is option B.

We know that

Question:

Answer:

The answer is the option (d). Rectangles, rhombus and square in a plane is a parallelogram but trapezium is not

Hence, (d) is correct

Question:

Answer:

The answer is the option (c)

From the above Venn diagram

Hence, the correct option is (C)

Question:

Answer:

The answer is the option (d)

R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis

Hence, the correct option is (d)

Question:

Answer:

The answer is the option (b).

Let C be the set of students who play cricket and T the set of students who play tennis.

Total number of students = 60 ⇒n(U)=60

Number of students who play cricket = 25 n(C)=25

Number of students who play tennis = 20 n(T)=20

Number of students who play both the games = 10

Number of students who play any one game

Number of students who play neither

Question:

Answer:

The answer is the option (b)

Total number of persons in a town = 840 n(U) = 840

Number of students who read Hindi = 450 n(H) = 450

Number of students who play English = 300 n(E) = 300

Number of students who read both = 200

Question:

If } and . Then

(A) (B) (C) X = Y (D)

Answer:

The answer is the option (a).

Given that

And

Here, it is clear that every element belonging to the X is also present in Y.

. Hence, the correct option is (A).

Question:

Answer:

Let p% of people watch a channel and q% of people watch another channel

So,

Now n(p) = 63.

So,

Hence, the correct option is (C).

Question:

If sets A and B are defined as , then

(A) A ∩ B = A (B) A ∩ B = B (C) A ∩ B = φ (D) A ∪ B = A

Answer:

The answer is option (c). Given that and

So, and

Thus, option C is correct.

Question:

If A and B are two sets, then A ∩ (A ∪ B) equals

(A) A (B) B (C) (D) (A ∪ B)

Answer:

The answer is the option (a). Let

Hence A is correct.

Question:

Answer:

The answer is the option (b).

Given that A ={1,3,5,7,9,11,13,15,17}

B = {2,4,6………..,18}

U=N={1,2,3,4,5,……..}

Question:

Answer:

The answer is the option (b).

Given that: S={x| x is a positive multiple of 3 < 100}

S = {3, 6, 9, 12, 15, 18 …..99}

n(S) = 33

T = { x| x is a prime number < 20}

T = {2, 3, 5, 7, 11, 13, 17, 19}

n(T) = 8

So, n(S) + n(T) = 33+8 =41

Hence, (b) is correct.

Question:

Answer:

The answer is option (c)

Let

Question:

When, then number of elements in P(A) is ______________.

Answer:

When, then number of elements in P(A) is 1

Here , n(A) = 0

Question:

Answer:

Given that A = {1,3,5}, B= {2,4,6} and C = {0,2,4,6,8}

Universal set of all given sets is U = {0, 1, 2, 3, 4, 5, 6, 8}

Question:

Answer:

Given that: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B ={2, 4, 6, 7} and C = {2, 3, 4, 8}

Question:

Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then

Answer:

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

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

Since B and M has same elements

M = B, So, is false

Question:

The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.

Answer:

The two sets do not contain same elements. Hence, false.

Question:

, where Q is the set of rational numbers and Z is the set of integers.

Answer:

Since every integer is a rational number

Hence true

Question:

Let sets R and T be defined as

Then T ⊂ R

Answer:

R = {………….., -8, -6, -4, -2, 0, 2, 4, 6, 8,…..}

And T= {……., -18, -12, -6, 0 , 6, 12, 18,…….}

Since every element of T is present in R. So,

Hence, the statement is true.

Question:

Answer:

Here A = { 0, 1, 2} B is a set having all real numbers from 0 to 2.

So,

Hence, the given statement is False.

Question:

Match the following sets for all sets A, B and C

(a)

(b)

(c)

(d)

(e)

(f)

Answer:

(I)

(II)

(iii)

(iv)

(v)

(vi)

So (i) – b , (ii) – c, (iii) – a, (iv) – (f), (v) - (d), (vi) – (e)

Sets are basically defined as a collection of objects belonging to a particular field or are of the same kind in a defined manner and could be differentiated from others for all at the same time or in the same sense.

For example- a group of days in a week will be the same for everyone, so, it is considered a set whereas a group of top ten favourite musicians in the world would be different for everyone as everyone has different choices, so this collection or group is not a set.

NCERT Exemplar Class 11 Maths chapter 1 solutions provided here for the NCERT books are very useful for Board exams as well as the JEE Main exams. Students can use NCERT Exemplar Class 11 Maths solutions chapter 1 PDF download for offline learning.

The topics included in the chapter are mentioned below:

- 1.1 Introduction
- 1.2 Sets and their Representations
- 1.3 The Empty Set
- 1.4 Finite and Infinite Sets
- 1.5 Equal Sets
- 1.6 Subsets
- 1.6.1 Subsets of a set of real numbers
- 1.6.2 Intervals as subsets of R
- 1.7 Power Set
- 1.8 Universal Set
- 1.9 Venn Diagrams
- 1.10 Operations on Sets
- 1.10.1 Union of sets
- 1.10.2 Intersection of sets
- 1.10.3 Difference of sets
- 1.11 Complement of a Set
- 1.12 Practical Problems on Union and Intersection of Two Sets

With NCERT Exemplar Class 11 Maths chapter 1 solutions, the students will learn about forming sets through a roaster and set builder method. This will help in various life situations to form combinations or groups of things belonging to the same category or are related to one another with a well-defined purpose. They also have wide application in mathematics for different subjects and are used in every field of mathematics in some or the other way. It also has its application in different programming languages and economic analysis, which will enable students to relate its use to real life. NCERT Exemplar Class 11 Maths solutions chapter 1 will also teach discipline to students through organizing and categorizing different things for better daily needs.

· Class 11 Maths NCERT Exemplar solutions Chapter 1 also provides two different methods for the representation of sets, i.e. roster or tabular form and set builder form both of which use different representations for displaying a set. The roster of the tabular method shows elements in a form, as A = {a, e, w, o, u}, but the same set in set-builder form will be represented as A = {a : a is a vowel in English language} which depicts that the element an of set A is a vowel of English language.

· NCERT Exemplar solutions for class 11 Maths chapter 1 also defines different types of the set such as empty set not having any member elements, finite set, having fixed/countable elements, infinite set, having uncountable member elements, equal sets have identical elements, power set, universal set, and subsets.

· NCERT Exemplar Class 11 Maths solutions chapter 1 also covers Venn diagrams and its application in different operations of the set, including union, intersection, and difference along with their detailed properties.

**Check Chapter-Wise NCERT Solutions of Book**

Chapter-1 | Sets |

Chapter-2 | |

Chapter-3 | |

Chapter-4 | |

Chapter-5 | |

Chapter-6 | |

Chapter-7 | |

Chapter-8 | |

Chapter-9 | |

Chapter-10 | |

Chapter-11 | |

Chapter-12 | |

Chapter-13 | |

Chapter-14 | |

Chapter-15 | |

Chapter-16 |

**Read more NCERT Solution subject wise -**

- NCERT Solutions for Class 11 Maths
- NCERT Solutions for Class 11 Physics
- NCERT Solutions for Class 11 Chemistry
- NCERT Solutions for Class 11 Biology

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Download EBook**Also, read NCERT Notes subject wise -**

- NCERT Notes for Class 11 Maths
- NCERT Notes for Class 11 Physics
- NCERT Notes for Class 11 Chemistry
- NCERT Notes for Class 11 Biology

**Also Check NCERT Books and NCERT Syllabus here:**

1. Which topics are covered in this chapter?

The chapter of sets covers everything related to sets like the types, the subsets, the Venn diagrams and practical problems related to sets.

2. Can these solutions be helpful for competitive exams?

Yes, these questions and NCERT Exemplar Class 11 Maths solutions chapter 1 are helpful for those who are preparing for engineering and other entrance exams.

3. How to make the most of these solutions?

These NCERT exemplar Class 11 Maths chapter 1 solutions can be used while practising the questions from the NCERT book. These solutions can also be a reference for checking the answers.

4. How many questions are solved in these solutions?

Our team has solved every exercise question that is present in the main exercise and also the ones in the additional questions.

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