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Linear programming class xii chapter 12, math assignment class xi ch -1 set theory, mathematics assignment.

Class - XI | Subject Mathematics | Chapter - 1

For non-medical /applied math students.

*******************************************************

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 : x 2  ≤ 10 ,   x  ∈ Z }     

a) {10, 11, 12, 13, 14, 15}   

b) 1, 4, 9, .........., 121}      

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

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

Ans: P(A) = {φ, {φ}, {1}, { φ, 1}}

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

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

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

then find n(S) + n(P)       Ans 41

Question 10

(a)  A ∩ (B - C) = (A ∩ B) - (A ∩ C)

(b) A - (B ∩ C) = (A - B) ⋃ (A - C)

Question 11

a)   A ⋃ (A ∩ B) = A   

b) (A ⋃ B) – B = A - B   

c) (A - B) ⋃ (A ∩ B = A

d)   A ⋃ (B - A) = A ⋃ B   

e) A - (A ∩ B) = A - B   

f) A ⋃ B) – B = A - B

Question 12

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

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 

Now we have  x ∈ B ⇒ x ∈ A     

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

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

Question 14

Question 15

Question 16

Question 17

(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 ? 

Question 18

(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 

Question 19

(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  

Question 20

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 ?

Solution Hint:

Question 21 (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.

Wonderful question and innovative ideas

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Why the cbse introduced and then withdrew continuous evaluation, the board had introduced continuous comprehensive evaluation for a holistic assessment of students in 2009 but discontinued it in 2017 as teachers weren't ready. will it work now.

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The CBSE and ISC Board’s formulae for the evaluating students in a year when board exams cannot be conducted are reminiscent of the CCE. If the CBSE will use the 30-30-40 formula, taking marks of the past three years, the ISC intends to consider marks attained over the past five years. Even as students and parents complain that considering internal test marks is unfair since “most students study only for the boards”, educationists feel that it might a good time to revive a method similar to the CCE to make education more holistic in the future.

Dr Akhil Shahani, managing director of the Thadomal Shahani Centre for Management and the Shahani Group, says that in the CCE, students were to be assessed based on their class performance, homework, submission of assigned projects, periodic tests and active participation in various activities conducted in class. Schools were told to implement CCE assessment as they saw fit. “Unfortunately, a majority of schools could not adapt to this new model as they did not know how to train faculty to change old methods of teaching. There were also complaints that students were not able to do well in standardised exams needed for admission into top colleges,” he says.

It’s no secret that admissions to leading colleges can be impacted by even one mark, which affects the overall percentage. With every state board having different marking methods, the CCE, say teachers, could not lead to standardised marks. “This method was revoked in 2017 and the CBSE reverted to the old model of year-end exams, which fuels the learning-by-rote method,” says Shahani.

Educators are hopeful that if the National Education Policy (NEP) gets rolled out by 2022, the shift towards value-based learning, instead of rote learning, will be more pronounced. “It will promote value-based learning since the motive of the NEP is continuous assessment instead of an annual examination,” says Dr Mohan Rao, professor and associate dean at IES Management College, Mumbai.

Teachers say that the CBSE and ISC Boards’ formulae have already prompted a change in the way students view school classes. Attendance is no longer only about clocking the minimum number of classes in Class 11 and 12 while attending tuition classes. Students realise that their participation in the virtual classroom and continuous assessment will matter. “After the CBSE spelt out the formula of 30-30-40, I see a positive change in the attitude of students towards attending classes online, unit tests and class work. Parents have also realised the importance of continuous assessment. I see a renewed interest in my classes,” says Geeta Bagai, a Class 10 teacher at Don Bosco School, New Delhi.

While the CCE is a promising shift, Kavita Sahay Kerawalla, vice-chairperson of the VIBGYOR Group of Schools, says that to incorporate continuous assessment, the study patterns will have to change and schools will need to use a variety of tools and strategies, such as tests, assignments, interviews, self-exploration, research projects, fieldwork, portfolios and examinations, from the start of the academic year to assess students. “This approach will give teachers a fair idea about the capabilities and potential of students and will give students more flexibility to be creative and not resort to rote learning,” she says.

Most teachers agree that continuous assessment will give schools the chance to allow flexibility in their teaching methods. “We can focus on the skill sets of students rather than only preparing them for the board exams,” says Sunita George, principal of Bombay Scottish School, Mahim, Mumbai.

However, schools and colleges are skeptical about whether this pattern of assessment will be welcomed by all. A parent of a Class 10 student says that most schools do not have teachers who are equipped to evaluate students through projects and tests. “Teachers are not trained well. Most of them follow the motto of rote learning where they merely dictate answers and expect students to reproduce them verbatim. How can such teachers be expected to assess the students creatively?” she asks.

Shahani stresses that the continuous study model needs specific guidelines and faculty training support from the authorities. “Additionally, top institutions still require students to score high marks in standardised entrance exams for admission. I fear that the new continuous assessment regime may suffer the same fate as the CBSE’s old CCE model unless the government provides further guidance and support on helping institutions adapt to it,” he says.