**UNIVERSITY EXAMINATIONS: 2017/2018**

**EXAMINATION FOR THE DIPLOMA IN BUSINESS INFORMATION **

**TECHNOLOGY **

**DBIT103 FOUNDATION OF MATHEMATICS**

**FULLTIME/PARTIME**

**DATE: AUGUST, 2018 TIME: 1 ½ HOURS**

**INSTRUCTIONS: Answer question One and ANY other two questions.**

**QUESTION ONE**

a) Define the following terms and give an example for each

i) Tautology

ii) Contradiction

iii) Contingency (9 Marks)

b) Determine the hypothesis and consequences for each of the following conditional

Statements. Then determine their truth values

i) The moon is square only if the sun rises in the east

ii) “If you do your homework, you will not be punished.” (6 Marks)

c) Construct a truth table for (~ p ∨ q) ∧ ~ q. (9 Marks)

d) Explain the following properties of functions (6Marks)

i) Injectives

ii) Surjectives.

iii) Bijectives

**QUESTION TWO**

a) Differentiate between the following terms and state an example for each

i) Propositional connectives

ii) Compound propositions (4Marks)

b) Given the following statement “If you study hard, then you will not fail in foundation of

mathematics examination”. Write its

i) Negation

ii) Contra positive

iii) Converse

iv) Inverse (4Marks)

c) Given the two sets: A={a, b} and B={1,2},

i) Find the Cartesian product of A and B.

ii) The Cartesian product of B and A (4Marks)

d) Differentiate between universal quantification and existential quantification (4Marks)

e) Express the statement “there is a number x such that when it is added to any number, the

result is that number, and if it is multiplied by any number, the result is x” as a logical

expression. (4Marks)

**QUESTION THREE**

a) Negate the following quantified statements (4Marks)

i) Every student in this class has visited Mombasa

ii) There is a student in this class with a kabambe phone

b) Find the domain and range of the following functions

c) Find the inverse of the following functions

i) f(x) = 2x + 3

ii) f(x) =

3

x

2+1

iii) f(x) =

4

2x

3+2

(9Marks)

**QUESTION FOUR**

a) Define the following terms giving examples of how each is represented (10Marks)

i) Real numbers

ii) Irrational numbers

iii) Rational numbers

iv) Universal set

v) Null set

b) Discuss any two properties of sets (2Marks)

d) Given the Sets:

A = {1, 2, 3, 4}

B = {5, 6, 7, 8}

C= {6, 7, 9}, find

i) A ∪ B ∪ C (2Marks)

ii) B ∩ C (2Marks)

iii) B

. ∩ (C ∩ A

,

) (4Marks)

c) State the following laws of set theory

i) commutative laws

ii) associative laws (4Marks)

**QUESTION FIVE**

a) Solve, write your answer in interval notation and graph the solution set. (4Marks)

b) Prove that if n is an integer and n

3 + 5 is odd, then n is even. Use (6Marks)

i) Proof by contradiction

ii) Indirect method of proof

c) State the following laws of set theory

i) commutative laws

ii) associative laws (4Marks)

d) Let f(x) = x + 2 and g(x) = 2x +1, find

i) (fog)(x) and

ii) (gof)(x) (6Marks)