Abstract Algebra (MATS2103)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 200
Year: 2018
THE UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
MATS203 CON TIN U OU S A S S ESSM ENT T ES T
ANSW E R . ALL Q U E S T IONS: A l l ste p s must b e neatl y pre s e n t e d
1. ( 1+3=4 mar ks)
(i) What do you understand by a mathematical statement?
(ii) (ii) Let p and q be statements. Show that ~ (p ⇒ q) ≡ p∆~ q
2.
If A. B and C are sets, such that A ⊆ C, prove that A
∩
(B - C)=∅ (3marks)
3.
(1 +3+ 3 = 7marks)
(i) Define a prime, p
(ii) Prove that if p is a prime and a, b ∈
ℤ
., and suppose p|ab, or p|b.
(iii) Let d ∈ ℕ
∗
, d > 1. Supposed d|(12k +33) and d|(4k + 10), for some k ∈ ℤ,
show that d=3
4.
If x ≥ 1, prove by mathematical induction that 1+ nx ≤ (1 + x)
n
,∈ ℕ (4marks)
5.
(1+7=8marks)
(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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