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MAS501S - MATHEMATIICAL STRUCTURES - 1ST OPP - JUNE 2023 |
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nAmlBIA unlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICSAND ACTUARIALSCIENCE
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 5
COURSECODE: MASS0lS
COURSENAME: MATHEMATICAL STRUCTURES
SESSION:JUNE 2023
DURATION: 180 MINUTES
PAPER:THEORY
MARKS: 100
EXAMINER
MODERATOR:
FIRSTOPPORTUNITYQUESTION PAPER
MR. B.EOBABUEKI
PROFESSORSUNDAY REJU
INSTRUCTIONS
1. Answer ALL questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLEMATERIALS
Non-programmable calculator without a cover.
THIS QUESTION PAPERCONSISTSOF 3 PAGES(excluding this front page)
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Question 1 (21 marks)
1.1 Do the following sums
1.1.1 2132.2245 +214.0245 +4432.4225 +21212.2445
1.1.2 6601.2367 -5535.26457
1.2 Do the following conversions
1.2.1 AB8.FE 16 to decimal
1.2.2 527.56 10 to octal correct to 3 octal places.
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(4)
(4)
(6)
(7)
Question 2 (15 marks)
2.1 Given that A, B, and C are subsets of a universal set S, draw a Venn diagram and
shade the subset (Au B) n C' .
(2)
2.2 Prove that P' n Q' is a subset of (Pu Q)' given that P and Q are subsets of Z .(6)
2.3 A survey of 100 youths gave the following information:
50 jog, 30 swim, and 35 cycle; 14 jog and swim; 7 swim and cycle; 9 jog and cycle; 3 take
part in all three activities.
2.3.1 Represent the given information in a Venn diagram.
(4)
2.3.2 How many youths jog but do not swim or cycle?
(1)
2.3.3 How many youths take part in only one of the three activities?
(1)
2.3.4 How many youths do not take part in any of the three activities?
(1)
Question 3 (12 marks)
3.1 Copy and complete the following truth table in your answer script: (---, means negation) (5)
p q r ---,pvr ---,r
F FT
TT F
FT F
T FT
pAqvr
---,(rV ---,P) (---,pI\\ ---,q) r
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3.2 If Jane does not cry or Paul works hard then, dad gets his salary and ma does not sell her
car.
Use the following variables to express the statement above in symbolic logic form:
(5)
j:
Jane will cry;
p:
Paul will work hard;
d: dad got his salary; m: ma sold her car
3.3 Write down the contra-positive version of the statement: If Peter plays soccer, then
Mary plays netball.
(2}
Question 4 (17 marks)
4.1 The following pseudocode is expected to read 1000 whole numbers and output the
average of only the even numbers.
START
INT
n = 0, num(n}, sum = 0, k = 1000, count= O
FLOAT
average
BINARY
even, odd, fraction
DOWHILE n <= 100
READ num(l}
IF num(n} = even
sum= sum+ num(n}
count= count+ 1
ELSE
ENDIF
ENDWHILE
average= sum/count
PRINT'The average is' AVERAGE
END
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There are errors in this pseudocode. Rewrite the pseudocode with the errors corrected.
(5)
4.2 Draw a flowchart that reads 1000 numbers and outputs the average of only the
numbers not less than 25.
(12)
Question 5 (20 marks)
- - ---
5.1 Draw the logic circuit of the Boolean expression E(A, B, C) =AB+ ABC+ (A+ B)C.
(7)
5.2 Simplify the Boolean expression B(x, y, z) = xy + x y + z + x(yz).
(5)
5.3 Study the following logic circuit:
A------i
B---------i
c------,
Draw the following table in your answer script and use the logic circuit to complete it.
(8)
A1
1
1
1
0
0
0
0
B
1
1
0
0
1
1
0
0
C
1
0
1
0
1
0
1
0
E
Question 6 (15 marks)
6.1 Prove that the sum of two even numbers is even.
(6)
6.2 Use mathematical induction to prove that the sum ofthe first n natural numbers is
-n(n+l).
(9)
2
END OF PAPER
TOTAL: 100 MARKS
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