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)
