Math Assignment Class XI Ch -1 Set Theory

Mathematics Assignment

Math Assignment  Class XI  Chapter 1  Set Theory, Extra and important questions on Set Theory useful for Mat and Applied Math students. 

Class - XI | Subject Mathematics | Chapter - 1

For Non-Medical /Applied Math Students

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Question 1

Write the following sets in tabular form

a){ x : x = 2n + 1 ; n ∈ N}    

b) {x : x – 1 = 0}      

c) {x : x = prime number and   x ≤ 7 ; x ∈ N    

d) {x : x ∈ I,  3x - 2 = 3}    

e) {x : x² ≤ 10 ,  x ∈ Z }     

Answers of Q 1
a	{3, 5, 7, 9, ........}
b	{1}
c	{ 2, 3, 5, 7}
d	φ
e	{0,  土1,  土2,  土3}

Question 2

Write the following in set builder form

a) {10, 11, 12, 13, 14, 15}   

b) 1, 4, 9, .........., 121}      

Answers of Q 2
a	{x : x ∈ N : 9 < x < 16
b	{x2 : x  ∈ N ; 1  ≤  x  ≤  10

Question 3

Write the subsets of the set A = {1, 2, {3}}  

Ans  φ, {1}, {2}, {{3}}, {1,2}, {1, {3}}, {2, {3}}, {1, 2, {3}}

Question 4

Write the proper subsets of A = {5, 10, 11, 15}  

Ans: Except { 5, 10, 11, 15}, all other subsets of A are proper subsets.

Question 5

Write the power set of A = { φ, 1}  

Ans: P(A) = {φ, {φ}, {1}, { φ, 1}}

Question 6

List all the subsets of set  {-1, 0, 1}  

Ans φ, {-1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}, {-1, 0, 1}

Question 7

From the sets given below select the equal and equivalent sets

A = {0, 1, 2}, B = {a, b},    C = {1, 0, 2},    

D = {3, 5, 9, 13}  E = {5, 25},  F = {1, d}

Ans Equal sets:  A and C,   Equivalent Sets : B, E and F ;   A and C

Question 8

Let S = {x: x is a positive multiple of 3, less than 100}

P= {x : x is a prime number less than 20} 

then find n(S) + n(P)       Ans 41

Question 9

Let A and B are two sets , show  A - B , A ∩ B, B - A in venn diagram.

Question 10

If A = {a, b, c, d. e}, B = {a, c, e, g}, C = {b, e, f, g} verify that

(a)  A ∩ (B - C) = (A ∩ B) - (A ∩ C)

(b) A - (B ∩ C) = (A - B) ⋃ (A - C)

Question 11

If A and B  are two sets then, prove that

a)   A ⋃(A ∩ B) = A   

Solution Hint:

LHS = A ⋃(A ∩ B) 

        = (A⋃A)∩(A⋃B) 

        = A∩(A⋃B) = A = RHS

b) (A ⋃ B) – B = A - B   

Solution Hint:

LHS = (A ⋃ B) – B 

        =  (A ⋃ B) ∩ B' 

        = (A∩ B')⋃(B∩ B') 

        = (A∩ B')⋃Φ 

        = A∩ B' = A - B = RHS

c) (A - B) ⋃ (A ∩ B) = A

Solution Hint

LHS = (A - B) ⋃ (A ∩ B) 

        = (A∩ B' )⋃ (A ∩ B) 

        = A∩(B'⋃B) = A∩U = A = RHS

d)  A ⋃ (B - A) = A ⋃ B   

Solution Hint

LHS = A ⋃ (B - A) 

        = A ⋃ (B ∩ A')

        =A ⋃ B ∩ A ⋃A' 

        = A ⋃ B ∩Φ = A ⋃ B

e) A - (A ∩ B) = A - B   

Solution Hint

LHS = A - (A ∩ B) 

        = A ∩ (A ∩ B)' 

        = A ∩(A' ⋃ B') 

         = (A ∩ A' )⋃(A ∩B') 

        = Φ ⋃ (A ∩B') 

        = (A ∩B') = A - B = RHS

f) A ⋃ B) – B = A - B

Solution Hint

LHS = A ⋃ B) – B 

        = A ⋃ B) ∩ B' 

        = (A∩B' ) ⋃ (B∩ B') 

        = (A - B)⋃Φ = A - B = Φ

Question 12

If A = {1, 2, 3, 4, 5},  B = {1, 3, 5, 7, 9}, C = {2, 3, 4}, verify that 

A - (B ⋃ C) = (A - B) ∩ (A - C)

Question 13

Show that for any two sets A and B, If A ⋂ B = A ⋃ B, then A = B

Solution

Let x ∈ A ⇒ x ∈ A ⋃ B

                ⇒ x ∈ A ⋂ B 

                ⇒ x ∈ A and B 

                ⇒ x ∈ B 

Now we have  x ∈ A ⇒ x ∈ B     

               ⇒ A ⊂ B  ............ (i)

Let x ∈ B ⇒ x ∈ A ⋃ B

                ⇒ x ∈ A ⋂ B 

                ⇒ x ∈ A and B 

                ⇒ x ∈ A 

Now we have  x ∈ B ⇒ x ∈ A     

               ⇒ B ⊂ A  ............ (ii)

From (i) and (ii) we have A = B

Question 14

In a class of 35 students, 24 like to play cricket and 16 like to play football. Also each student like to play at least one of the two games. How many like to play both Cricket and Football.   Answer: 5

Question 15

In a survey of 400 students in the school, 100 were taking apple juice, 150 were taking orange juice. Find how many students were taking neither apple juice not orange juice.   

Answer:  225

Question 16

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of  58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ? 

Answer 9

Question 17

In a group of 200 students, it was found that 120 study maths, 90 study Physics, 70 study Chemistry, 40 study Maths and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Maths, 20 study  all the three subject. Find the number of students.

(i) Who study all the three subjects ?  

(ii) Who study maths only ?  

(iii) Who study one of the three subject ? 

(iv) Who study two of the three subjects ? 

Answers of Q 17
(i)	20
(ii)	a = 50
(iii)	100
(iv)	60

Question 18

Out of 100 students, 15 passed in english, 12 passed in Maths, 8 passed in science, 6 in English and Maths, 7 in Maths and Science, 4 in English and science, 4 in all three. Find how many passed in

(i) English and Maths but not in science  

(ii) Maths and Science but not in English

(iii) Maths only.  

(iv) More than one subject only 

Answers of Q 18
(i)	2
(ii)	3
(iii)	3
(iv)	9

Question 19

In a group of 50 students , 17 students studying French , 13 English, 15 Sanskrit, 9 studying French and English, 4 Studying English and Sanskrit, 5 studying French and Sanskrit, 3 studying all the three subjects. Find the number of students who study.

(i) Only French, 

(ii) Only English  

(iii) Only Sanskrit 

(iv) English and Sanskrit but not French 

v) French and Sanskrit but not English  

(vi) French and English but not Sanskrit 

(Vii) At least one of the three languages 

(viii) None of the three languages 

Answers of Q 19
(i)	6
(ii)	3
(iii)	9
(iv)	1
(v)	2
(vi)	6
(vii)	30
(viii)	20

Question 20

In a group of 100 people 65 like to play Cricket, 40 like to play Tennis and 55 like to play Volleyball. All of them like to play at least one of three games. If 25 like to play Both Cricket and Tennis 24 like to play both Tennis and Volleyball and 22 like to play Both Cricket and Volleyball then

a) How many like to play all three games? 

b) How many like to play Cricket only? 

c) How many like to play Tennis only?

Answers of Q 20
(i)	11 Players like all 3 games
(ii)	29 like cricket only
(iii)	2 like tennis only

Solution Hint:

C∩T = a + b = 25

T∩V = a + d = 24

C∩V = a + c = 22

P(C⋃T⋃V) = n(C) + n(T) + n(V) - n(C∩T) - n(T∩V) - n(V∩T + n(C∩T∩V)

100 = 65 + 40 + 55 - 25 - 24 - 22 + a

100 = 89 + a

11 = a

b = 25 - 11 = 14

d = 24 - 11 = 13

c = 22 - 11 = 11

No. of player play all the games a = 11

n(Cricket only) = 65 - a - b - c = 65 - 11 - 14 - 11 = 29

n(Tennis only) = 40 - a - b - d = 40 - 11 - 14 - 13 = 2

n(Volleyball only) = 55 - a - c - d = 55 - 11 - 11 - 13 = 20

Question 22 (DAV Final 2023-24)

You are the manager of a local supermarket, and you have three sets of products that represent different categories of items in your store

Set A = (1, 3, 4, 5, 7, 9} represents the inventory of fruits.

Set B = {0, 2, 4, 6} represents the inventory of dairy products.

Set C = (4, 7, 8, 9} represents the inventory of customer-favourite items.

Your goal is to optimize your supermarket's inventory and customer satisfaction. You plan to use set operations to make informed decisions.

(i) Which items can you offer to your customers if you combine the inventories of fruits (A) and dairy products (B) ?

(ii) You want to stock items that are both fruits (A) and customer favourites (C). Find the items.

(iii) To maximize sales, you want to offer products that are either fruits (A) or items that are both dairy products (B) and customer favourites (C). Find the items.

(iv) You are considering a special promotion and want to offer items that are available in all categories: fruits (A), dary products (B) and customer favourites (C). Find the items.

Question 21 (DAV SQP 2024)

Given, A = {x:  -1 < x ≤ 5 , x ∈ R} and

           B = {x:  - 4 < x ≤ 3 , x ∈ R}

Find: (i)  A ⋂ B     (ii) A' ⋂ B     (iii) A - B

Also represent each result on different number lines 

Solution Hint: 

(i)  A ⋂ B = {x:  -1 < x ≤ 3 , x ∈ R}

(ii) A' ⋂ B = {x:  -4 < x ≤ -1 , x ∈ R}

(iii) A - B = {x:  3 < x ≤ 5 , x ∈ R}

Question 22 (DAV FQP 2025)

Two finite sets have m and n elements. Total number of subsets of first set is 112 more than the total number of subsets of second set. Find the value of m and n .

Solution:

Let two sets are A and B

Number of subsets of set A = 2^m   

Number of subsets of set B = 2ⁿ   

ATQ    2^m   -  2ⁿ   = 112

2^m   - 2ⁿ = 112

2^m   -  2ⁿ = 2⁴ x (2³ – 1)

2^m   -  2ⁿ = 2⁷ -  2⁴

m = 7 and n = 4

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