Daily question

[ankita]

no of blue balls is 4

[ankita]

880 females are single and young.

[Kanika]

52% watched none of the three matches.

[Kanika]

REDUCTION IN ELECTRICITY CONSUMTION IS 2.5

[Amit Goyal]

Mar 22-25, 2009
1. Let X ={0,1}. List the elements of {P(A) |A ∈ P(X)}
2. Let X = ∅. List the elements of {P(A) |A ∈ P(X)}
3. Write the 16 elements of P(P({0,1}))
4. Find a set X with an element x such that x ∈  X and x⊂ X.

P(.) denotes the power set of .

[DEEPTI]

1) P(X)={{0,1},{0},{1},FI}

IF A={0,1} THEN P(A)={{0,1},{0},{1},FI}

IF A={0} THEN P(A)={{0},FI}

IF A ={1} THEN P(A)={{1},FI}

IF A=FI THEN P(A)={FI}


3)P{P(X)}={{{0}} ,{{1}} ,{{0,1}} ,{FI} ,{{0,1},{0}}, {{0,1},{1}} ,{{0,1}.FI} ,{{0}.{1}},{{0},FI}, {{1},FI}, {{0,1},{0},{1}}, {{0,1},{0},FI}, {{0},{1}.FI}, {{0,1},{1},FI},
{{0,1},{0},{1},FI} ,FI}



2)X= NULL SET

P(X)={ FI}

NOW A BELONGS TO P(X).THUS A=FI

THEN P(A)={ FI}



4)SUPPOSE X={ FI}

THEN FI BELONGS TO X

ALSO,FI IS SUBSET OF EVERY SET .THUS FI BELONGS TO SUBSET OF X
 

[deepti]

earlier bijlee was consumng (5,5).now after imposition of surcharge in excess of 4 units , bijle will consume atleast 4 units of bboth electricity n widgets because otherwise she would not be able to spend her whole income.now upto 4 units she would spend 8 rs . now in 2s she wld be able to consume 0.666 units of both goods.thus consumption is 4.666 units.therefore her consumption is reduced by 0.333 units...

[Amit Goyal]

26-28 March, 2009

1) Find the values of a and b such that the function de…fined by
f(x)= 5, if x ≤ 2
= ax + b, if 2 < x < 10
= 21, if x ≥ 10
is a continuous function.

2) Find all the points of discontinuity of f defi…ned by f(x) = |x|-|x + 1|.

3) Suppose f and g are two discontinuous function, then f + g is necessarily discontinuous. Prove or disprove.

[deepti]

1)  problem 1

in the first situation restaurant A  vl either attract both consumers or vl not be  able to attract both consumers.

p(of attracting both customers)=1/2
p(of not attracting both)=1/2

therefore xpcted profit=1/2 . 2-1/2.2=0

situation 2:

customer1  chooses A and 2 choosesA

CUSTOMER 1 CHOOSES A AND 2 CHOOSES B

BOTH CHOOSES B

CUSTOMER I CHOOSES B AND 2 CHOOSES A


XPCTD PROFIT:1/2.1/2.2+1/2.1/2.(-2)+1/2.1/2(1-1)+1/2.1/2.(1-1)=0

problem2:


in situation 1 expected profit is 0

in situation 2:

1/2.1/2.3+1/2.1/2.(-3)+1/2.1/2.(1-2)+1/2.1/2.(-1+1)=-1/4

[deepti]

3)a part
 BY CHARGIN 6000RS FOR BIG BED FOOM AND 4000 RS FOR SMALL ROOM ,UTILITY FOR BOTH INDIVIDUALS VL BE SAME.THIS IS PARETO EFFECIENT ALLOCATION AS IF I CHARGE 5000 FOR SMALL ROOM THEN UTILITY OF PRSON HAVING SMALL ROOM IS WORSE OFF AND PERSON HAVING BIG ROOM IS BETTER OFF.SIMILARLY IF I CHARGE 6000 FOR BIG ROOM THEN 1 PRSN IS N=MADE BETTER OFF AND OTHER WORSE OFF.

b part

no there is nosuch allocation.As rent is 10000 and if an individual pay 10000 then he vl get negative utility.

[Amit Goyal]

29 March, 2009
One of A,B,C and D has committed a crime with help of another one of them. Here are the statements given by 4 individuals. Statement of criminal and his accomplice are false and those of remaining are true:
A: if B is guilty,then C must be innocent.
B: if A is innocent, then C must be guilty.
C: if B was killer, then D must have had nothing to do with crime.
D: i am innocent
Which one of four is criminal & who was his accomplice?

[Khushboo]

1-  % of group that watched none of the three sports = 52%

2-  P(both labwork and specialist) = 0.05 or 5%

3- No of blue balls= 4

4-  f(x) is a continuous function, therefore, value of a= 2 and b= 1.

5-  f(x) = |x|-|x + 1|.
     It implies that
                  -1 , if x≥0
                   1 , if x<0
     Clearly f(x), being a constant function for x>0 and x<0, is continuous for all x>0 and all x<0 except at x=0.

[Amit Goyal]

30th March, 2009
A monopolist faces a demand curve p=1/q for q>0. His marginal cost is 0, What will be the equilibrium output and price?

[ankita]

a=2, b=1

[ankita]

for this monopolist the mr curve is the x axis as the mr is 0 that implies that the change in output has no effect on tr.. also the elasticity is 1.. total revenus is 1.. p=1/q and q=1/p as pq=1....

[Kanika]

D is the killer and B is his accomplice,hence A and c are innocent.If A and c are innocent,their statements should be true.A says "if B is guilty then c must be innocent"-which is true also C says "if B was the killer then D must have had nothing to do with the crime" ,so its contrapositive should also be true that is "if D has something to do with the crime then B is not the killer",which also implies that D is the killer.Also B and D should be telling a lie so the negation of their statements must be true.Hence if B says"if A is innocent ,then c must be guilty" so its negation which is "A  is innocent and c is not guilty" which is true,also the negation of D's statement should be true which is"i am not innocent",which is true as we have proved above that he is the killer.

[Amit Goyal]

31st March, 2009

In a certain bank the positions of cashier, manager and teller are held by Brown, Jones and Smith, though not necessarily respectively. The teller, who was an only child earns the least. Smith, who married Brown's sister, earns more than the manager.
What position does each man fill?

[Kanika]

smith is the cashier,jones is the teller and brown is the manager.

[ankita]

smith is the cashier, jones is the teller and brown is the manager

[Amit Goyal]

Logic problems (While posting answers use the code given on top of the question)
040109(1)
Erratic Behavior occurs when an individual acts in a manner that lacks consistency, regularity, and uniformity. Which situation below is the best example of Erratic Behavior?
a. Julia cannot contain her anger whenever the subject of local politics is discussed.
b. Martin has just been told that he is being laid off. Before leaving his supervisor’s office, he punches a hole in the door.
c. Rhonda has visited the dealership several times, but she still cannot decide which car
to buy.
d. In the past month, Jeffrey, who has been a model employee for three years, has repeatedly
called in sick, forgotten important meetings, and been verbally abusive to colleagues.

040209(1)
Establishing a Power of Attorney occurs when a legal document is created that gives one individual the authority to act for another. Which situation below is the best example of Establishing a Power of Attorney?
a. Louise is selling her house and she hires a lawyer to review the contract.
b. Simone’s mother can no longer get to the bank to cash her checks and make deposits, so she has taken legal steps to enable Simone to do these things for her.
c. Jack’s father is elderly and Jack thinks he is no longer able to make decisions for himself.
d. At her daughter’s urging,Mrs. Lenox opens up a retirement account with the local bank.

040309(1)
Posthumous Publication occurs when a book is published after the author’s death.
Which situation below is the best example of Posthumous Publication?
a. Richard’s illness took his life before he was able to enjoy the amazing early reviews of his novel.
b. Melissa’s publisher cancels her book contract after she fails to deliver the manuscript
on time.
c. Clarence never thought he’d live to see the third book in his trilogy published.
d. Elizabeth is honored with a prestigious literary award for her writing career and her daughter accepts the award on behalf of her deceased mother.

040409(1)
A Tiebreaker is an additional contest or period of play designed to establish a winner
among tied contestants. Which situation below is the best example of a Tiebreaker?
a. At halftime, the score is tied at 28.
b. Mary and Megan have each scored three goals in the game.
c. The referee tosses a coin to decide which team will have possession of the ball first.
d. The Sharks and the Bears each finished with 14 points, and they are now battling it out in a five-minute overtime.

040509(1)
An Informal Gathering occurs when a group of people get together in a casual, relaxed
manner. Which situation below is the best example of an Informal Gathering?
a. The book club meets on the first Thursday evening of every month.
b. After finding out about his promotion, Jeremy and a few coworkers decide to go out for a quick drink after work.
c. Mary sends out 25 invitations for the bridal shower she is giving for her sister.
d. Whenever she eats at the Mexican restaurant, Clara seems to run into Peter.

040609(1)
In the Maple Hill school district, a Five-Day Suspension occurs when a student is not permitted to attend school for five days for (1) physically assaulting another student, a teacher, or a school employee or (2) willfully destructing or defacing school property. Which situation below is the best example of a Five-Day Suspension?
a. Lillian gets caught cheating on a math test for the second time and is suspended from
school.
b. Marc is asked to leave the classroom due to his constant disruptions.
c. Franny uses spray paint to write derogatory comments on the locker room wall and she is given a suspension.
d. Ms. Farmer tells her class that students who fail the midterm exam will be expected to
stay after school for tutoring help.