BIT1206  DISCRETE MATHEMATICS KCA Past Paper

UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN
INFORMATION TECHNOLOGY AND BACHELOR OF BUSINESS
INFORMATION TECHNOLOGY
BIT1206 DISCRETE MATHEMATICS
FULL TIME/PART TIME
DATE: DECEMBER, 2016 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.

QUESTION ONE (30 MARKS)
a) Define the following terms
i) A set (1 Mark)
ii) A function (1 Mark)
iii) A relation (1 Mark)
iv) Domain of a relation

QUESTION TWO (20 MARKS)
a) Construct a relation on the set
{1,2,3,4,5}
that is reflexive, anti symmetric and transitive

QUESTION THREE (20 MARKS)
a). Define the following terms as used in logic theory
i) A proposition (1 Mark)
ii) A closed statement (1 Mark)
iii) A truth table (1 Mark)
iv) Logical connective (1 Mark)
v) Negation

d) Test the validity of the following arguments
“If you find this difficult then you have not done your home work. You have done your
homework. Therefore, you won’t find it difficult”.

QUESTION FOUR (20 MARKS)

QUESTION FIVE (20 Marks)
a) Use Venn diagrams to show that

(6 Marks)
b) One hundred students were asked whether they had subscribed to any of three mobile
telephone networks, Airtel, Safaricom and Orange. The results were:35 had Airtel line,38 had
Safaricom line, 31 had Orange line, 18 had Airtel and Safaricom, 9 had Airtel and Orange, 4 had
Orange and Safaricom and 23 were not connected to any of the lines;
i. Determine the number of students who have all the three lines (6 Marks)
ii. Draw a Venn diagram to represent the survey (5 Marks)
iii. How many students had Airtel and Safaricom but not Orange (1 Mark)
iv. How many students had Safaricom or Orange but not Airtel (1 Mark)
v. How many students had at most two lines

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