# DBIT 103 FOUNDATIONS OF MATHEMATICS. UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE DIPLOMA IN BUSINESS INFORMATION
TECHNOLOGY
DBIT 103 FOUNDATIONS OF MATHEMATICS
SPECIAL/SUPPLEMENTARY EXAMINATION
DATE: JULY, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.

QUESTION ONE (compulsory)

(a) Using relevant examples, briefly explain the following terms as used in set theory
(i) Union of two sets (2 Marks)
(ii) Universal set (2 Marks)
(iii)Set difference (2 Marks)
(b) Distinguish between the following terms
(i) Power of a set and class as used in set theory (4 Marks)
(ii) A Relation and a function (4 Marks)
(c) Given that Set U= For each relation, determine the domain and the range and use matrix method to represent them
(4 Marks)
(e) Find the inverse of the following function (Total: 30 Marks)
QUESTION TWO
(a) Illustrate the following laws as used in set theory

(i) Distributive laws (2 Marks)
(ii) De’ Morgans laws (2 Marks)
(iii) Commutative laws (2 Marks)
(b) Consider the following relations and use the arrow diagrams to determine whether they are
functions or not and give a reason. QUESTION THREE
(a)Distinguish between the following terms
(i) A Tautology and a Contradiction (4 Marks)
(ii) Logic and an Axiom (4 Marks)
(b)Fill in the following table and make a comment on. (Total: 20 Marks)
QUESTION FOUR
(a)There are 3 methods that can be used to represent relations, identify and explain them. (9
Marks)
(b) (i)Distinguish between a symmetric relation and non-symmetric relation (asymmetric)
(2 Marks)
(ii)Explain what is meant by a Bijective function (2 Marks)
(c) Find the domain and the range of the following function. (Total: 20 Marks)
QUESTION FIVE
(a)Explain what is meant by a rational number. (1 mark)
(b) Rationalize the denominator (3 Marks)

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