# DBIT103  FOUNDATIONS OF MATHEMATICS .

UNIVERSITY EXAMINATIONS: 2015/2016
EXAMINATION FOR THE DIPLOMA IN BUSINESS/ INFORMATION
TECHNOLOGY
DBIT103 FOUNDATIONS OF MATHEMATICS
DATE: AUGUST 2016 TIME: 1½HOURS

QUESTION ONE
(a) Using examples, briefly explain the following terms as used in set theory

i. A class (1 Mark)
ii. Equality of sets (1 Mark)
iii. Compliment of a set (1 Mark)
(b ) Given that set

above, we can derive the following relations;

For each relation,
(a)Determine the domain and the range (2 Marks)
(b) Use the arrow diagram to represent relations R1 and R2 (2 Marks)

(c) Represent relations R1 and R2 above, in matrix form (2 Marks)
QUESTION TWO
(a) (i)Define the term irrational number (2 Marks)
(ii)Show that the following numbers are irrational

(b) (i) Explain when directed graphs are used to represent relations (2 Marks)
(ii)Given the following relations, use the directed diagrams to represent them

QUESTION THREE
(a) Rationalize the denominator

(c) Distinguish between a function and a relation (4 Marks)
QUESTION FOUR
(a) Distinguish between a proposition and a negation (2 Marks)
(b) Fill in the missing gaps in the following tables and make a comment on each

(d)Distinguish between one to one function property and onto function property (4 Marks)
QUESTION FIVE
(a) (i)Distinguish between the Domain and the Range of a relation (2 Marks)
(ii) Outline how a relation is represented in a matrix form (3 Marks)
(b) Using the principle of mathematical induction, show that

(d) Demonstrate the following laws as used in set theory
(i)Distributive laws
(ii)Associative laws

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