eco 134 sec 8 quiz 1

8/2/2019 ECO 134 Sec 8 Quiz 1

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SECTION ATHERE ARE FIVE QUESTIONS IN THIS SECTION. ANSWER ALL QUESTIONS.

EACH QUESTION IS 1 MARK

1. Suppose we want to build an analytical model for the following situation: corporatetax on companies has been increased by the Government. As a result, firms profitwill be affected. In order to make up for the loss in profit, firms will change the price of their goods and services. Which equation best defines the relation between profit and price of firm due to a change in corporate tax rate?

A. Definitional EquationB. Behavioural EquationC. Conditional EquationAnswer:

B. The section specifically mentioned firms will change price of goods &

services in response to the increase of tax rate. Hence, this describesbehavior.

2. Suppose A={x│x R} and set B={1,2,3}. What will∈ be theCartesian product of AxB?

A. A x B = (x,1), (x,2), (x,3)B. A x B= {(x,1), (x,2), (x,3)}C. A x B = { (a,b) │a R and b {1,2,3}}∈ ∈

D. A x B = {(a,b) │(a,b) R}∈Answer:C. A={x|x R} & B={1,2,3}. Correct answer is C because Cartesianԑ

product is an order pair where the 1st element will be any real no. & 2nd

element will be either 1,2 or 3. This also tells why option D is incorrect

because in option D element b is said to be ANY real no which is not true

since b consists of only 1,2 or 3.

3. Which of the following does not represent a function?

A. y = 2xB. y= x2 + 10C. y = 10/xD. y 2 + x2=50Answer:

D. function is for every value of x, we should have one value of y.

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8/2/2019 ECO 134 Sec 8 Quiz 1


The option where every value of x DOES NOT give 1 value of y is option

D.

Y2+x2=50

Or, y2=50-x2

Or, y= ±(50-x2)(1/2)

So each value of x gives the 2 values of y, one which is +ve and one

which is –ve.

4. The range of the function f(x) = (x+6)2 is:

A. (0 ≤ f(x) < ∞)

B. ( 6 ≤ f(x) < ∞)C. ( - 6 ≤ f(x) < ∞ )D. The set of all Real NumbersAnswer:

A. range means possible values that f(x) can take for given x values

(Domain). Since in the Q domain is not given, it means x can take any

real no.

Notice the function is quadratic, so whatever the value of x we put, f(x)

will be a positive value. Only when x=6, we have f(x) =0. Hence the

lowest value of range is 0 while the maximum value can be anything

depending on which value x takes. Hence, correct answer choice isoption A.

5. The solution of {( 8√(M)n x M(x+4) (x + 4) )/ M2y – 8} YM + (x3 – 3) is:

A. {( 8√(M)n x M(x+4) (x + 4) )} + (x3 – 3)

B. (M N/8 +16x – 2y +8 ) YM

C. (M N/8 +16x – 2y +8 ) YM – 3+ x3

D. None of the aboveAnswer:

C.

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8/2/2019 ECO 134 Sec 8 Quiz 1


SECTION BTHERE IS ONLY ONE QUESTION IN THIS SECTION. ANSWER IT FULLY. THE

TOTAL MARKS FOR THIS SECTION IS 15.

1 a) i. What is the difference between a mathematical model and an economic model?2.5 MARKSAnswer:have been provided in lecture notes

ii. Prove that the smallest subset of any set is the empty set { }.2.5 MARKS

Answer:this had also been provided in lecture notes. Nevertheless, here is the proof:Let us consider subsets of set S. To prove that smallest subset of any set is the empty set (Ø

or {} ) we need to use proof by contradiction method.Assume Ø is not a subset of S (i.e Ø S ). This means the empty set must contain at least 1ԑ element that is not in set S. but this cannot be possible because empty set does not have anyelements in it. Hence Ø has to be a subset of S (or any set).

b) Suppose you are given the following information: U = { x N∈ │N is consists of positive integers and x ≤ 10}A= { x N∈ │x is odd}B = { x N∈ │x is a prime number} where prime number is any number that is divisible by 1 and itself only. Note: prime numbers are always greater than 1.

U= { x N|N is positive integer & x≤10}ԑ

It was clearly mentioned in class that 0 is neither positive nor negative. Also since N is +veinteger, it means x is any no. greater than 0 & last no. is 10.Therefore, U={1,2,3,4,5,6,7,8,9,10}A={ x N|x is odd}ԑ

N has already described in the universal set to be a positive integer & less than equal to 10.And since x is odd no set A will consist of +ve integers that are odd.A={1,3,5,7,9}B={x N|x is a prime no}ԑ

I have even defined what a prince no is in the question. It is any no that can be divided by

the number 1 and itself only. And since x is in N, it means we have to consider prime no.only from 1 to 10.Therefore, B={2,3,5,7}Therefore my sets are:U={1,2,3,4,5,6,7,8,9,10}A={1,3,5,7,9}B={2,3,5,7}

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8/2/2019 ECO 134 Sec 8 Quiz 1


i) Construct the above information in a Venn Diagram. Show separately the elements of AUB and A∩B.

4 MARKS

Answer:

It was mentioned in Question that you have to show elements of AuB &A∩B separately.So,AuB={1,2,3,5,7,9}A∩B={ 3,5,7}

ii) Suppose you are told C={ x N∈ │x is even}. Prove the distributive law using theabove details.

3 MARKS

Answer:i) C={x N|x is even}ԑ

Therefore, the elements in C will be determined in the same way as the elements in setA. but now, we are going to consider even nos. only between 1 & 10.Therefore, C={2,4,6,8,10}Distributive Law is:Au(B∩C)=(AUB) ∩(AUC)A∩(BuC)= (A∩B)u(A∩C)Students were required to write both parts of the law.however, you had to prove any part of the law since time in the exam was limited.

U={1,2,3,4,5,6,7,8,9,10}A={1,3,5,7,9}

B={2,3,5,7}C={2,4,6,8,10}B∩C={2}AuB={1,2,3,5,7,9}AuC={1,2,3,4,5,6,7,8,9,10}

1st part of the law : Au(B∩C)=(AUB) ∩(AUC)L.H.S: Au(B∩C)= {1,2,3,5,7,9}R.H.S: (AUB) ∩(AUC)

= {1,2,3,5,7,9}∩{1,2,3,4,5,6,7,8,9,10}=(1,2,3,5,7,9}

L.H.S= R.H.S2nd part of law: A∩(BuC)= (A∩B)u(A∩C)LHS: A∩(BuC)

={1,3,5,7,9} ∩{2,3,4,5,6,7,8,10}={3,5,7}

RHS: (A∩B)u(A∩C)={3,5,7}u{}={3,5,7}

LHS=RHS

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8/2/2019 ECO 134 Sec 8 Quiz 1


iii) Suppose D = {(3,5), (-0.5, 4), (x, 0), (-12, -5)}, what should be the domain of x in orderto ensure set D represents a function? Explain carefully.

3 MARKSAnswer:

D={(3,5), (-0.5,4), (x,0), (-12,-5)}In order to ensure set D represent a function we need to ensure every value of xgives one value of y. therefore, domain of x will consist of any real no. exceptfor x≠3, x≠-0.5 & x≠-12. This is because we already have y values for these 3x values in set D. if x had been any of these 3 no. we would have got 2 y valuesfrom one x value which will not make set D a function.

THE END

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eco 134 sec 8 quiz 1

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