# DBIT103  FOUNDATIONS OF MATHEMATICS.

UNIVERSITY EXAMINATIONS: 2017/2018
EXAMINATION FOR THE DIPLOMA IN BUSINESS INFORMATION
TECHNOLOGY
DBIT 103: FOUNDATIONS OF MATHEMATICS
FULLTIME/PARTTIME
DATE: APRIL, 2018 TIME: 2 HOURS
INSTRUCTIONS: Answer any Question one and any other two questions.

QUESTION ONE (Compulsory)
a) Using relevant examples, distinguish between the following terms as used in set theory
(i) A subset and equality of sets [2 Marks]
(ii) Set difference and disjoint sets [2 Marks]
(iii) A sample and universal set [2 Marks]
b) Given that Set U=
1,2,3,4,5,6,7,8,9
Set
A 2,3,4,7,8
and set B=
2,4,6,7,9
(i) Show that (U
A)
(B
A) =A [4 Marks]
(ii) Determine set
AxB [2 Marks]

(iii) Determine set
A B [2 Marks]
(iv) The power of set B [2 Marks]
c) Define the term complex number hence work out the following

QUESTION TWO
a) Discuss FOUR types of relations [8 Marks]
b) Explain THREE methods of representing relations [6 Marks]
c) By using illustrations, distinguish between a Contradiction and a Tautology [2 Marks)]
d) Work out the following

QUESTION THREE
a) Differentiate between the domain and the range of a relation [4 Marks]
b) Use the arrow diagram and matrix form to represent the following relation

c) Distinguish between a rational number and a complex number [4 Marks]
d) Fill in the missing columns in following table

QUESTION FOUR
a) Differentiate between a proposition and an axiom as used in logic [4 Marks]
b) By the principle of mathematical induction, show that

QUESTION FIVE
a) Use directed graph to represent the following relation

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