“Discrete Structures”
“Q2: Determine whether each of these functions from {a,b,c,d} to itself is onto and/or one-to-one. a) f(a)=b, f(b)=a, f(c)=c, f(d)=d
a

b

c

d

a

b

c

d

a

b

c

d
a

b

c

d

The above Function is both one-to-one and onto, therefore Its called a BIJECTION Function

b) f(a)=b, f(b)=b, f(c)=d, f(d)=c
a

b

c

d

a

b

c

d

a

b

c

d
a

b

c

d

The above Function is

c) a

b

c

d
a

b

c

d
a

b

c

d
a

b

c

d
f(a)=d, f(b)=b, f(c)=c, f(d)=d

The above Function is Neither On to nor one-to-one
“Q6: Take two sets A and B of your choice and determine the following: A = {0,1,2,3,4}
B = {2,4,6,8,10}
a) A∪B
= {0,1,2,3,4,6,8,10}

b) A∩B
= {2,4}

c) A-B
= {0,1,3}

d) B-A
= {6,8,10}

“Q4: Let S = {-1,0,2,4,7}. Find f(S) if the following conditions are followed” a)fx=1
As there are no values to substitute x with therefore this function shall remain the same regardless of the number of values

b)fx=2x+1
One by one the above mentioned set values are put into the function =2-1+1 =22+1 =5
= 1 =24+1 =9
=20+1
=1 S = {1, 1, 5, 9, 15}

=27+1
=15

c) fx=|x5|
Putting the set values into the above equation
|-15| = 15

05 =0

25 =0.4 S= {0.5, 0, 0.4, 0.8, 1.4}

45=0.8

75=1.4

e) fx=|x2+13|
Putting the values of the Set S in the above equations

-12+13=23

02+13=13
S = {2/3, 1/3, 5/3, 17/3, 50/3} 22+13=53

42+13=173

72+13=503

“Q8: Construct a proof that
a) If m is odd, then m^2 is odd
b) for all integers m and n, if m is even and n is odd, the m+n is odd” a) If m is odd, then m=2k + 1
We have to prove that m^2 is odd, so squaring the above mentioned equation we get =(2k + 1)^2
= 4k2+1+2(2k)(1)
=4k2+1+4k
Put in any odd value in the above equation
= 452+1+4(5)
=425+1+20
=121

Hence proved that the square of the value of m which is odd is also odd

b) Since m is odd (2k+1)
And n is even (2k)
Also since m+n is to be proved odd
=m+n
=2k + 1 + 2k
=4k + 1
Put any integer in the above function
4(5) + 1 4(4) + 1
=21 =21

4(10) + 1 4(7) + 1
=41 =29

“Q7: For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises.”

...1. Define Proposition and provide at least five (5) Proposition and Non-Propositional statements.
Proposition refers to either (a) the "content" or "meaning" of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence
Examples of Propositions
1.The sun is shining.
2. The sum of two prime numbers is even.
3. 3+4=7
4. It rained in Austin, TX, on October 30, 1999.
5. x+y > 10
Examples of Non-Propositional Statements
1.Do you want to go to the movies?
2.Clean up your room.
3.2x= 2 +x
4.This sentence is false.
5.
2. What
The negation operator is a unary operator which, when applied to a proposition p, changes the truth value of p. That is, the negation of a proposition p, denoted by: p, is the proposition that is false when p is true and true when p is false. For example, if p is the statement \I understand this", then its negation would be \I do not understand this" or \It is not the case that I understand this." Another notation commonly used for the negation of p is p. Generally, an appropriately inserted \not" or removed \not" is sufficient to negate a simple statement.
The conjunction operator is the binary operator which, when applied to two propositions p and q, yields the proposition \p and q", denoted p ^ q. The conjunction p ^ q of p and q is the proposition that is true when both p and q are true and false otherwise.
The disjunction operator is the binary operator...

...12.4).
12.11 You are required to create a conceptual data model of the data requirements for a company that specializes in IT training. The Company has 30 instructors and can handle up to 100 trainees per training session. The Company offers five advanced technology courses, each of which is taught by a teaching team of two or more instructors. Each instructor is assigned to a maximum of two teaching teams or may be assigned to do research. Each trainee undertakes one advanced technology course per training session.
(a) Identify the main entity types for the company.
(b) Identify the main relationship types and specify the multiplicity for each relationship. State any assumptions you make about the data.
(c) Using your answers for (a) and (b), draw a single ER diagram to represent the data requirements for the company.
Chapter 13 Extended Entity-Relationship Modelling
13.7- Describe the two main constraints that apply to a specialization/generalization relationship.
There are two constraints that may apply to a superclass/subclass relationship called participation constraints and disjoint constraints.
Participation constraint determines whether every occurrence in the superclass must participate as a member of a subclass. A participation constraint may be mandatory or optional. A superclass/subclass relationship with a mandatory participation specifies that every entity occurrence in the superclass...

...between the importance of the ‘white’ and Aboriginal races at the time in that area. Jane Harrison is using this contrast to show the reader how much of an impact that time was and to educate the reader of the thoughts and feelings of those who were put through those circumstances.
3. Scene 1 (B)
a) How is the hessian used in this scene and what is it symbolic of?
The hessian is used to cover up the damage of their ‘humpy’ from the floods, which is symbolic of the ‘white’ race covering up the damage they had done to the Aboriginal population, as hessian is not completely secure, it is a weak fabric.
4. Scene 2 (A): Oh, Errol
a) What is the significance of Gladys’ success when answering the Pick-A-Box questions?
Gladys’ success in answering the trivial questions signifies her intelligence and understanding.
5. Scene 2 (B):
a) Why is Nan so suspicious of Errol and the encyclopedias?
Nan is suspicious because very rarely would a ‘whitefella’ come around offering service to their population. She is suspicious because she may feel that this is a scam on her family, taking their hard earned ‘picking money’.
6. Scene 3: Lino
a) Errol suggests Dolly come to the city to work. Why would this be difficult for her?
This would be difficult for Dolly because of her strong connection to the land and family she belongs to. She would not want to leave them.
b) How does this scene develop the concept of belonging in the play?...

...Answer to Questions and Problems
1) In a strain gauge bridge, what does (a) a negative reading on the zero centered meters imply? (b) a positive reading on the zero centered meters imply?
- A negative reading on the zero centered meter implies that the strain gauge is under compression. Whereas, a positive reading implies that the strain gauge is under tensile / tension.
2) Beside strain gauge transducers, what other transducers can be used in a bridge circuit?
- Besides strain gauge transducers, many materials can be used as a makeshift bridge circuit. Materials such as photoelectric which absorbs light and convert the light energy to electrical energy. Etc..
3) Before any strain is applied, the bridge is balanced with R1= 1k, R2= 100, R= 625 and R= 0. Determine the strain if the bridge was rebalanced with R= 2.4.
Given: R1= 1k R= 0
R2= 100 R= 2.4.
R3= 625 Req’d: Rsf.
Solution:
4) The bridge from the previous problem is balanced this with R1= 3k , R2= 100, R= 1250 and R= 0. Determine the strain if the bridge was rebalanced with R= 6.4.
Given: R1= 3k R= 0
R2= 100 R= 6.4.
R3= 1250
Solution:
Rs= (100/3k)(1250)
Rs= 41.67
Rs= (100/3k)(6.4)
Rs= 0.21
Rsf= 41.67 + 0.21
Rsf= 41.88
5) Determine the value of Rx from the balanced bridge shown in the figure below.
Solution:
*From the balance bridge about we can say that:
20(10)=Rx(5)
Rx= 40...

...QUESTIONS AND ANSWERS
1. Evaluate the internal and external environment and analyze major obstacles to making this merger successful.
To answer satisfactorily this question, students must prepare, at a minimum, the weaknesses (internal) and threats (external) parts of a SWOT analysis. Students, based on their educational and professional background, may create many obstacles, but the major strategic issues are outlined below:
Internal Obstacles
a) Culture--Started in 1983, America West Airlines (AWA) is a much newer airline and is the only post-deregulation startup to survive. It is known as a lower fare, full-service airline that has achieved profitability as recently as 1Q and 2Q of FY05.
In contrast, US Airways (USA) is larger and a legacy carrier and has been in existence since 1939. It has not been profitable, on a fiscal year basis, since 1999. The company has been in bankruptcy twice since 2002.
In evaluating each company's history and its current standing within the industry, a clash of employee cultures must be considered. The merged airline will be headed by existing AWA senior management. However, a smaller, younger, more fluid, and profitable carrier merging with a larger, unprofitable, legacy carrier has the potential for two organizational problems. First, the merged company has elected to utilize the US Airways name, a perceived stronger brand image than AWA, and this decision...

...judgment is affected by the visual feedback you are receiving from the thermometers according to the (C) A. representational heuristic. B. algebraic heuristic. C. availability heuristic. D. algebraic algorithm. 11. Early psychologists interested in intelligence assumed that there was a single, general factor for mental ability, which they called (C) A. fluid intelligence B. the performance factor C. the g-factor D. emotional intelligence 12. If you score at the 75th percentile on a standardized test, it means that (C) A.75 of those who took the test scored better than you did. B.25 of those who took the test scored less than you did. C.75 of those who took the test scored the same or less than you did. D.you answered 75 of the questions correctly. 13. Mr. and Mrs. Proudparent are beaming because their son, little Newton, has been selected for a gifted children program at school. They think Newton is a genius. What sort of advice do they need to hear (B) A.Youngsters with a 130-140 IQ tend to be very maladjusted B.Most gifted children do not go on to make genius-level, major contributions to society that earn them eminence. C.They should prepare to be famous, based on their parentage of Newton. D.They should be warned that gifted children often have deficits in practical intelligence. 14. Jackson had a huge breakfast this morning and is still feeling stuffed when he arrives at work. However, one of his colleagues has brought some delicious-looking...

...| 480 | 60 | -120 |
90 | 100 | 650 | 750 | 1.11 | 7.22 | 7.22 | 150 | 540 | 60 | -210 |
100 | 100 | 900 | 1,000 | 1 | 9 | 9 | 250 | 600 | 60 | -400 |
c. Determine the profit maximizing level of output. Explain how you arrived at that conclusion.
The profit maximizing level is when Profit equals Marginal Cost or (P=MC.) It can also be: MC=MR so it is the production level corresponding to 60. So Q=50. In other words for an output of 50, the Marginal Cost or (MC) =6. Therefore, the firm will output 50.
d. What is the total profit at the profit maximizing level of output? How does that compare to profit at other levels of output?
You would have to look at the total profit resulting from producing 50 widgets to answer the question. In this case profit would be equal to 0. This is because when the total profit is 0 (as it should be) we are producing the optimal level without any dead weight losses.
e. What is the lowest price that Winsome Widgets will accept and continue to produce in the short run? Explain.
The slope of the total revenue curve is marginal revenue and the slope of the total cost curve is marginal cost. Economic profit (the difference between total revenue and total cost) is maximized where marginal revenue equals marginal cost. This is consistent with the marginal decision rule, which holds that a profit-maximizing firm should increase output until the marginal benefit of an additional unit equals the...

...framework that can be used to conduct a business portfolio analysis
3) What are the differences between a marketing plan and an IMC plan?
4) What information does an IMC plan derive from the marketing plan?
5) In the context of communication planning, what is a situation analysis, and how does it differ from a SWOT analysis?
6) What is typically included in an IMC plan?
7) What is the first step in developing an IMC plan, and why is it so important?
8) Discuss thoroughly the second step of an IMC plan.
9) Why should we talk about segmentation/targeting/positioning in developing an IMC plan? Support your answer by giving examples.
10) Discuss 4 managerial methods of budget setting in the context of marketing communications.
11) What is the best method of budget setting in the context of marketing communications? Explain your answer....