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Syllabus

what is set - builder form and roster form

rates of return in are as follows:

A. B

Year 1. 10. 15

Year2. 12. 16

Using matrix notation, determine:

(i) Annual return of each year if he invests 50,000 and 80,000 in the securities for two years

(ii) Investment in each security for 2 years if he receives returns of 40,000 and 44,000 in two years respectively.

## What will be the best reference books for class 11 cbse?

what is the formula of n(A-B) and n(B-A)

can anyone provide me with class 11 c++ sumita arora solutions

What is an arbitrary element of a set? Explain.

prove A-B = A intersection B complement

prove that (A-B) U (B-A) =(A U B) - (A intersection B)

Two finite sets have m and n elements. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Find the valuesof m and n.In a survey of 100 students, the number of students studying the

various languages were found to be English only 18, English but not

Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and

Hindi 8, Number of no language 24. Find

i) How many students were studying Hindi?

ii) How many students were studying English and Hindi ?

If U is the set of all digits in our decimal system ,A={x:x is prime} B={x:x^2 <25}

find (AUB)'

1.A survey of 500 television viewers produced the given information;285 watch football;195 watch hockey;115 watch cricket;70 watch football and hockey;45 watch football and cricket ;50 do not watch any of three games.How many watch exactly one of the three games ?

In a school there are 200 students. 100 play cricket, 50 play hockey and 60 play basketball.30 students play both cricket and hockey, and 35 play both hockey and basketball. 45 play both basketball and cricket.

Find Out:-

a.)What is the maximum number of students who play at least one game?

b.)What is the maximum number of students who play all the three games?

c.)What is the minimum number of students playing atleast one game?

d.)What is the number of student playing all the three games?

In an exam, 80% passed in math, 72% passed in science, and 13% failed in both, If 312 students passed in both the subjects. Find the total number of students who appeared in the exam.

Let A ={x:x

^{3}+1=0};B={x:x^{2}-x+1=0} .Find A(intersection) B when (i) x is real (ii) x is not real.nwhat is the formula for n(AUBUCUD) /

(i) n(A intersection B) (ii) n(A) (iii) n(B)

A and B are two sets such that n(A-B)=20+x, n(B-A)=3x and n(A ∩B)=x+1.Draw a Venn diagram to illustrate this information.Find (i)the value of x (ii)n(AUB)

If A and B be two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in A ∪ B ? Find, also the maximum number of elements in A ∪ B ?

Let A,B be any two sets.Using properties of sets prove that -

(i) (A - B) U B = A U B

(ii) (A U B) - A= B - A

Draw Venn diagrams of :-

1. A-(BUC)

2.AU(B∩C)

n(A-B)=30, n (B-A)=18 and n(AuB)=50

find n(AnB)

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 3 men got medals in all three sports ,how many received medals in exactly 2 of the sports

If x belongs to A and A belongs to B, then x Belongs to B? Determine whether true or false and explain.

answer is:-

False, Consider A = {{1},2}

clearly, 1belongs to A and A belongs to B but 1 doen't belong to B

So, x belong to A and A belongs to B need not imply that x belongs to B.

SIr Please explain and give suitable example to make me understand.prove that :

A-(BnC)=(A-B)U(A-C)

A and B are two sets then prove that A minus B union B is equal to A union B.

Show that AUB(A union B) = A Intersection B implies A=B.

(a) A'

(b) B'

(c) AVB

(d) A - B.

1. In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% buy C. 5% buy AB, 3% buy BC and 4% buy AC. If 2% families buy all the three, find the number of families which buy i) A only ii) B only iii) none of A,BC.

a survey shows that 63% of americans like cheese whereas 76% like apples.If x% of americans like both cheese and apples,find the value of x.

rnplz explain in very a easy step.....

WHAT IS TRIVIAL AND NON.TRIVIAL SUBSET ??

3.In a survey of 25 students, it was found that 15 had taken mathematics,12 had taken Physics and 11 had taken chemistry.5 had takenMathematics and Chemistry,9 had taken mathematics and Physics,4 had taken Chemistry and Physics and 3 had taken all the three subjects. Find the number of students that hadShow that An(B-C)=(AnB)-(AnC)

sir can you prove the de morgan's law using venn diagram?

7. In a survey of 100 people it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A B, 10 read magazine AC 5 read magazine B and C and 3 read all the three. Find:i) How many read none of the magazines?ii) How many read magazine C only?

_{alpha} =(ax : x is the element of W} then W_{3}intersection W_{5 is}## Best books for cbse class 11 commerce students?

i) number of boys who play at least one of the games.

ii) number of boys who none of the games.

iii) number of boys who play football but not cricket.

iv) number of boys playing only hockey.

v) number of boys playing cricket but not hockey.

suppose A

_{1}, A_{2},....,A_{30}are 30 sets each with 5 elements and B_{1}, B_{2},...., B_{n}are n sets each with 3 elements. let union ofA_{1}, A_{2},....,A_{30}= union ofB_{1}, B_{2},...., B_{n}=S. Each element of S belongs to 10 of A's and 9 of B's. find n.WHAT DOES IT MEAN????????????

(a)A-B

(b) A

(c) B

(d) (AUB)-B

wat are d uses of sets in our daily life?

A-B=A delta (A intersection B)

IN A TOWN OF 10,000 FAMILIES IT WAS FOUND THAT 40% FAMILIES BUY NEWSPAPER A, 20% FAMILIES BUY NEWSPAPER B , AND 10% FAMILIES BUY NEWSPAPER C, 5% FAMILIES BUY A AND B , 3% BUY B AND C AND 4% BUY A AND C .IF 2% FAMILIES BUY ALL THE NEWSPAPERS FIND THE NUMBER OF FAMILIES WHICH BUY

1. A ONLY 2. B ONLY 3. NONE OF A ,B , AND C.

write in set builder form

{-4,4}

IF P(A)=P(B) SHOW THAT A=B

find the value of (A U B U C) ∩ (A ∩ B' ∩ C') ∩ C'

Hi

Prove That : cos6A = 32cos^6A - 48cos^4A + 18cos^2A - 1.

Write in set builder form.

B= {23,29,31,37,41,43,47}

There are 20 students in a chemistry class and 30 students in a physics class. find the number of students which are either in physics or in chemistry class in the following cases:

a)two classes meet at the same hour. (hint: n(Câˆ©P) =Î¦)

b)The two classes meet at different hours and 10 students are enrolled in both the courses. (hint: n(Câˆ©P)=10)

if A intersection B dash is equal to null set, then show that A is equal to A intersection B, and hence show that A is a subset of B. please help.

In a survey of 400 students in a school ,100 were listed as taking apple juice ,150 were listed as taking orange juice and 75 were listed as taking both apple as well as orange juice .Find how many students were taking neither apple juice nor orange juice.

for what value of x {x=x^2;x belongs to R}

for that your answer is

We have,

x^{2 }=x⇒x^{2 }-x= 0 ⇒x(x- 1) = 0 ⇒x= 0 or 1So there are two values of

xthat is 0 and 1 as both of them belongs to RWhat if we take 1=x/x^2 and if we substitute x=0 then it becomes 1/0 which is undefined.

Please explain why x=0

Verify De Morgan's law by using venn's diagram.

prove that A intersection (B-C) = (A intersection B) - (A intersection C)

a and b are two sets such that

n(a-b)=20+x

n(b-a)=3x

n(a∩b) =x+1 if n(a)= n(b)

the value of x

show that if ais A subset B,Then C-B is subset of C-A

Q1if A,B,C are three sets then proove that A∩(BC)=(A∩B)(A∩C)

Q2let A,B, and C be the sets such that AUB=AUC and A∩B=A∩C show that B=C

let U ={x ∈ N: x<10} ,A = {x ∈ N: 5 < x^{2}< 50} and B= {x ∈ N is a prime number <10} Draw a Venn Diagram to show the relationship between the given sets .Hence list the elements of the following sets i] A' ii] B'iii]A-B iv] A∩B'

Let A,B,and C be the sets such that AUB

= AUC and A intersection B and A intersection B = A intesection C show that

B=C

How do we prove it without using the Venn diagram?

In a beauty contest, half the number of judges voted for Miss A, 2/3 voted for Miss B, 20 voted for both and 6 did not vote for neither Miss A nor Miss B. Find how many judges , in all, were present there?

bhak ye sab kya satta batta kar raha hai?

Let A = {0,1,2,3,4} and B={1,3,4} . Write down all the proper subsets of A, which are super sets of B..

In a class 18 students took physics, 23 took chemistry, 24 took maths, out of them 13 took chemistry and mathematics, 12 took physics and chemistry, 11 took physics and mathmetics. if 6 were offered all the three subjects find :

1. Total number of students in class

2. How many took maths but not chemistrty

3. How many took exactly one of the three subjects

What is the difference between

andbelongs to?subsetwrite the set in set builder form S=( 1,3,9,27)

if A=( 2x:x belongs to N}, B = { 3x; x belongs to N}, C={ 5x: x belongs to N}, then find ( A intersection B) intersection C.

in a class of 60 students,23 play hockey,15 play basketball,20 play cricket and 7 play hockey and basketball,5 play cricket and basketball,4 play hockeyand cricket,15 do not play any of the three games. find the number of students who

1- play all the three games

2-play hockey but not cricket

3-play hockey and cricket both,but not basketball

A= set of all government hospitals in a city

Out of 2000 employees in a office 48 % preferred cofee, 54% liked tea , 64% used to smoke . Out of th etotal employee 28% used cofee and tea , 32% used tea and smoke and 30% prefered cofee and smoke and only 6% did none of these . The number having all th ethrree is ?

what is set ?

Using properties of sets prove the statements given:-

(i) For all sets A and B, AU(B-A) = AUB

(ii) For all sets A and B, A-(A-B) = AintersectionB

(iii) For all sets A and B, (AUB)-B = A-B

what is an improper subset?

1. Prove A intersection (A U B)' = phi

2. Prove that if A U B = C and A intersection B = phi, then C - B = A.

3. In ao town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper, 10% families buy newspaper C, 5% buy A and B, 3% buy B and C, 4% buy A and C, If 2% buy all three papers, then find the number of families which buy newspaper A only.

in a class of 25 student , 12 have taken maths,8 have taken maths but not biology.find the number of student who are taken maths and biology and the number of those who have taken biology but not maths .each student have taken either maths or biology or both?

Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than that of the total no. of subsets of the second set. Find the values of m and n.

At a certain conference of 100 people there are 29 Indian women and 23 Indian men . Out of these Indian people 4 are doctor and 24 are either men or doctors . There are no foriegn doctors. The number of women doctors attending the conference is ?

Of the members of three athletic teams in a certain school, 21 in are in basketball team, 26 in a hockey team and 29 in the football team.14 paly hockey and basketball and 8 play in all the three games, how many members are there in all