 |
MAS501S - MATHEMATIICAL STRUCTURES - 2ND OPP - JULY 2023 |
|
|
1 Page 1 |
▲back to top |
nAmlBIA UnlVERSITY
OF SCIEn CE Ano TECHn OLOGY
FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND ACTUARIAL SCIENCE
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 5
COURSE CODE: MASS0lS
COURSE NAME: MATHEMATICAL STRUCTURES
SESSION: JULY 2023
DURATION: 180 MINUTES
PAPER: THEORY
MARKS: 100
SUPPLEMENTARY/SECONDOPPORTUNITYQUESTION PAPER
EXAMINER
MR. B.EOBABUEKI
MODERATOR:
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 PAPER CONSISTS OF 3 PAGES (excluding this front page)
|
|
2 Page 2 |
▲back to top |
Question 1 (26 marks)
1.1 Do the following sums in the indicated number systems:
1.1.1 2122.0223 + 2212.213 + 21212.02123 + 222.22223
(5)
1.1.2 6623.3657 -4644.36627
(4)
1.2 Do the following conversions:
1.2.1 3465.32 8 to base 10 correct to 2 decimal places.
(4)
1.2.2 523.67 10 to base 8 correct to 4 octal places.
(6)
1.3 Perform the following conversions directly.
1.3.1 A2D0.2AF;6 to binary
(4)
1.3.2 100111000.0111 2 to octal
(3)
Question 2 (20 marks)
2.1 Write down what subset is represented by each of the following Venn diagrams:
2.1.1
(2)
2.1.2
(2)
Page 1 of 3
|
|
3 Page 3 |
▲back to top |
2.2 Define each of the following terminologies as used in set theory:
Subset, Power set, and Direct sum of two sets.
(6)
2.3 State the two D'Morgan's Laws for sets. No proof required.
(4)
2.4 Given that A and Bare subsets of S, prove that A' u B' is a subset of (An B)'. (6)
Question 3 (14 marks)
3.1 Write the following compound statement in logic symbolic form: "If the rain falls and
the sun shines, then John will bring Mary along if she gets her new shoes". (Remember
to state your four variables in this case.)
(5)
r:
rain falls;
s:
sun shines;
j:
John brings Mary;
m: Mary gets new shoes
3.2 Copy and complete the following truth table: (Note that --, means negation)
(5)
A
B
C
T
F
T
T
T
F
F
T
T
F
F
F
T
F
F
CA--,B
(BvC) -,(Av B) -,(A AB AC)
3.3 Use a truth table to investigate whether the following statements are logically
equivalent or not:
Statement 1: "All the intelligent students passed"
Statement 2: "A student that did not pass is not intelligent"
(Hint: Let "student passed be p and let student is intelligent be q")
(4)
Question 4 (12 marks)
There are 100 positive whole numbers. Some of the numbers are even and the others odd.
Write a pseudocode that finds and prints the average of only the odd numbers.
(12)
Page2 of 3
|
|
4 Page 4 |
▲back to top |
Question 5 (17 marks)
5.1 Draw the logic circuit of the Boolean expression E(A,B,C) =AB+ A+ BC+ ABC.
(7)
5.2 Simplify the Boolean expression B(x,y,z) = x+ y+ x yz + x(y+ z).
(5)
5.3 Study the following logic circuit:
A-----6---l
s----+--~
C----+--+---1
Draw the following table in your answer script and use the logic circuit to complete it.
(5)
A
1
0
1
1
0
B
1
1
0
0
0
C
1
1
1
0
0
E
Question 6 (11 marks)
6.1 Prove that the sum of two even natural numbers is even.
(5)
6.2 Use mathematical induction to prove that the sum of the first n odd natural numbers is
n2 .
(6)
End of paper
Total marks: 100
Page 3 of 3