Abstract Algebra (MATS2103)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 200
Year: 2018
THE UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
TEST
D
EPARTMENT
: Mathematics and Computer Science
C
OURSE
I
NSTRUCTOR
: Fomboh nee NFORBA M.
M
ONTH
:
C
OURSE
C
ODE
& N
UMBER
:
MATS 2103
Y
EAR
: 2018
C
OURSE
T
ITLE
:
Abstract Algebra
D
ATE
C
REDIT
V
ALUE
:
Six Credits
T
IME
A
LLOWED
: 1:30 hours
1. 10 marks
(i) If A. B and C are sets such that A ⊂ C, prove that A − B = A ∩ ( C − B)
(ii) a) What do you understand by a Mathematical statement
b) What is a tautology?
c) Write down the truth table of the proposition ~ (p ⇒ q) ⇒ (pVq) and hence determine whether or not it is a
tautology. (3, 1, 1, 5.)
2. 6marks
(i) Define a prime, p.
(ii) What do you understand by a | b
(iii) Let d > 1 and d is prime. Suppose d|(35n + 26) and d|(7n + 3) for some n ∈ ℤ, show that
d = 11.
(1, 1, 5marks)
3. 6marks
(i) State the principle of Mathematical Induction and hence
(ii) use it to prove that (1 + x)(l + x
2
)(1 + x
4
)• • • (1 + .r
2n-1
) =
(1, 5)
4. 13marks
(i) Define the g.c.d., d, of two integers a and b.
(ii) a)Use the Euclidean Algorithm to find d, the g.c.d. of 1073 and 814 and
b) express it in the form 1073x + 814y =d: x,y ∈ ℤ. Hence.
c) find the general solution of the equation 1073x + 814y = 74 d)Show that there are no positive integer solution
(1, 3, 2, 4, 3 marks)
GOOD LUCK
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