# BCU102  FOUNDATIONS OF MATHEMATICS.

UNIVERSITY EXAMINATIONS: 2018/2019
EXAMINATION FOR THE DEGREE OF BACHELOR OF BUSINESS
INFORMATION TECHNOLOGY
BCU102 FOUNDATIONS OF MATHEMATICS
DISTANCE LEARNING
DATE: APRIL, 2019 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.

QUESTION ONE [30 MARKS]
a) Distinguish between a finite set and infinite set as used in set theory, giving an example
in each case.

QUESTION TWO [20 MARKS]
a) Define the following terms
i. A set [ 1 Mark]
ii. A subset [ 1 Mark]
iii. Absolute complement [1 Mark]
iv. Venn-diagram [ 1 Mark]
v. A relation [1 Mark]

b) Show by truth table that the following statement formula is a tautology:

QUESTION THREE [20 MARKS]
a) Use truth table to text the validity of the following argument.
If I enter the poodle den, then I will carry my electric poodle prod or my can of mace.
I am carrying my electric poodle prod but not my can of mace.
Therefore, I will enter the poodle den. [10 Marks]

b) Write the converse, contrapositive and inverse of the following statement
“If it today is Saturday, then I will go for a walk”
[3 marks]
c) Prove by mathematical induction that
7  5
n
is divisible by
3
for all integers
n  0

QUESTION FOUR [20 MARKS]

b) In a class of
50
students.
30
study Mathematics,
18
study Electronics,
26
study
Accounting ,
9
study Mathematics and Electronics ,
16
study Mathematics and
Accounting,
8
study Electronics and Accounting, 47 study at least one of the three
subjects.
i. How many students study none of the three subjects? [2 Marks]
ii. How many study students study all of the three subjects? [4 Marks]
iii. Present the information in a Venn diagram. [4 Marks]
iv How many students study Mathematics or Electronics but not Accounting?
[2 Marks]
QUESTION FIVE [20 MARKS]
a) Define the following terms
i) Onto function [2 Marks]
ii) One-to-one function [2 Marks]
iii) Bijection function

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