Abstract Algebra (MATS2103)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 200
Year: 2015
THE UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
MATS203 CONTINOUS ASSESSMENT TEST
ANSWER ALL QUESTIONS: All steps must be neatly presented.
1. (1 +3=5 marks)
(i) what do you understand by a mathematical statement?
(ii) let p and q be statements. Show that ~
⇒
≡ ∧ ~
2. if A, B and C are sets,such that A⊑ . Prove that A∩ − =∅ and that A-B=A∩(C-B).
3. (1 + 5+5 = 11 marks).
(i) Define a prime, p.
(ii) Prove that if p is a prime and a,b∈ ℤ and suppose p
|
|
or p
|
|
.
(iii) let d∈ ℕ
*
, d>1. Suppose d
|
12 + 33
|
and d
|
4 + 10
|
, for some k∈ ℤ, show that d=3.
4. if x≥ 1, prove by mathematical induction that 1+nx≤ 1 +
, ∀" ∈ ℕ (5 marks)
5. (1+7=8 marks)
(i) What do you understand by the g.c.d. of two integers a and b?
(ii) Use the Euclidean algorithm to find, d the g.c.d of 7200 and 3132 and express it in the form
d=7200x+3132y. x,y∈ ℤ*
GOOD LUCK.
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