# Logical Analysis and Problem Solving

PROGRAMME

BSc (Hon) Computing and BEng Software Engineering Foundation Year
DATE
28thJanuary 2022
MODULE CODE
CTF3202
MODULE TITLE
Logical Analysis and Problem Solving
ASSESSMENT TYPE
Coursework
WEIGHTING
60%
STUDENT NAME

STUDENT ID

LEARNING OUTCOME:
LO3: Apply statistical principles to discern meaningful information based on a given scenario.
LO4: Demonstrate the use of algebra to solve given problems

[ASSIGNMENT INSTRUCTIONS]: This Assignment consists of three sections, and you must attempt to solve all the questions. Marks the corresponding questions are shown in the square brackets (on the right-hand side of each question). You must show all your calculations or graphs (Charts) as required otherwise zero mark will be allocated.
Section 1[ALGEBRA AND LOGIC GATES]: Show all necessary calculations.
1. Problem 1. Consider the following circuit that implements the 2-input function H(A, B):


Fill in the truth table for H:

Problem 2. Give a sum-of-products expression for each of the following circuits:


Problem 3. Solve the following equations system: 
2×1 + 6×2 + 4×3 = 18
5×1 + 6×2 + 4×3 = 24
-2×1 + x2 + 3×3 = 3

4. A foundation student bought a mobile phone and smart watch for a total of, excluding VAT (value added tax), paying 3 times as much for the mobile phone
as for the smart watch.
Write an expression to show the total cost in terms of the cost of the smart watch. 
What was the cost of each item? 
Calculate the VAT on the mobile phone, assuming a VAT rate of 14% 
5. Find the value of k to satisfy the equation referring to the discharge of water from a tank



6. Construct a chart giving values of and to satisfy the equation the range of being 5 to 100.(Use Excel) 

7. Construct a chart giving values of and to satisfy the equation the range of being 2 to 50. (Use Excel) 
8. Consider the following:
An online trading company wants to offer discounts to new customers. The company has recently emailed discount code to the customers. New customer must have a discount code to be eligible but returning customer are not eligible for a discount.
Let
A = Returning Customer
B = Discount Code
(a) Draw a truth table to represent when a customer has a discount. 
(b) From your truth table in (a) produce a Boolean expression to represent discounted customer (Q) for the trading company. 

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Section 2[Statistics]
9. The data below shows the monthly rent for 24 students: 1500, 1350, 350, 1200, 850, 900, 1500, 1150, 1500, 900, 1400, 1100, 1250, 600,610, 960, 890, 1325, 900, 800, 2550, 495, 1200, 690.
(a) Create a relative frequency distribution table using 7 classes 
(b) Use your table in (a) to produce a histogram to represent your data 

10. The following is a frequency table showing the ages of members of a symphony orchestra for young adults.
Age Frequency
15 2
16 5
17 11
18 9
19 14
20 13
21 10
22 13
Find the sample mean and median of the ages of the 77 members of the symphony. 
Section 3 [Flowchart and Algorithm Development]
11. Given the following list of steps in the admission process:
Search for a school
Prepare for the admission test and write test
Did you pass the exam?
Submit necessary documents and get admission
End
Are seats available?
Start
Re-arrange the above steps in the correct order and use MS Visio to draw a flowchart for the admission process. 

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12. Construct an algorithm that has as input an integer points and and a point and which produces as output the product


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