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MAS501S - MATHEMATICAL STRUCTURES - 1ST OPP - JUNE 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science ; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM; 07BOSC
LEVEL: 5
COURSE CODE: MAS501S
COURSE NAME: MATHEMATICAL STRUCTURES
SESSION: JUNE 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Mr B.E OBABUEKI
MODERATOR:
Prof S.A REJU
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations where necessary.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (excluding this front page)
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Question 1 (15 marks)
1.1 Subtract the number 7F.ABCDEF,, from the number F'D.3256,, .
(4)
1.2
Convert the number 245.3, to base 7 correct to 2 places after the point.
(7)
1.3
Use the grouping of digits to convert 30F.4£2,, to octal.
(4)
Question 2 (28 marks)
2.1
Let Q={1,2,3,4,5,6,7,8,9,a,b,c,d,e} be a universal set and let A ={1,3,5,7,9,b,d},
B={2,4,6,7,9,a,b,c} and C = {2,5,7,9,a,b} be subsets of Q.
2cded Draw a Venn diagram to represent this information.
(7)
2.1.2 Write down the power set PLAN BOC).
(4)
2.2 Among the 133 students at school, 44 take Geography, 48 take Biology, 32 take
Mathematics, 8 take both Geography and Biology, 9 take Geography and
Mathematics, 7 take Biology and Mathematics. 30 students take none of the three
subjects.
Zdel Draw a Venn diagram to represent this information.
(5)
2.2.2 Use the formula
nGUBUM)=n(G)+n(B)+nM)-n(GO B)-n(GOM)-n(BaAM)+n(GABNM)
to determine n(GABOM).
(3)
2.23 How many students take Geography or Biology?
(2)
2.2.4 How many students take Biology and Mathematics but not Geography?
(1)
2.3
Given that A and B are subsets of the same universal set, prove that
(A UBY CAB’.
(6)
Question 3 (10 marks)
3.1
Consider the following statements
p:
Peter went to school
q:
Queen ate an apple
r:
Russel missed his soccer practice
a:
Agnes cried.
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Write the statement If Peter did not go to school and Queen ate an apple, then either
Russel missed his soccer practice or Agnes did not cry in symbolic logic.
(5)
3.2
Use a truth table to determine whether the two statements (4’v B)’ and A” B’ are
contradictions, a tautology, equivalent or none of these.
(5)
Question 4 (17 marks)
4.1 Write a pseudocode that reads the names, gender and ages of 1000 persons and outputs
the average age of the males.
(10)
4.2
Draw a flow chart that solves the linear equation ax+b=c and outputs the result.
Your program must test whether a= 0.
(7)
Question 5 (15 marks)
5.1
Draw the logic circuit for the Boolean expression ECX,Y,Z) =XYZ+XYZ +XY.
(6)
5.2
Express A+ B+ABC+A+BC+B inasum of products form.
(5)
5.3
Copy the table below and use the following logic circuit to complete it:
(4)
:
—))—
Py >
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Question 6 (15 marks)
6.1
Use mathematical induction to prove that the sum of the first 7 odd natural numbers
isn.
(7)
6.2
Prove that the product of two odd numbers is odd.
(8)
END OF PAPER.
Total Marks 100
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