UNIVERSITY EXAMINATIONS: 2012/2013
FIRST YEAR EXAMINATION FOR THE BACHELOR OF SCIENCE
IN INFORMATION TECHNOLOGY
BIT 1206 DISCRETE MATHEMATICS
DATE: AUGUST, 2013 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other TWO Questions
QUESTION ONE
a) Consider the following data for 120 mathematics students at a college concerning
the languages French, German and Russian:
65 study French, 45 study German, 42 study Russian, 20 study French and
German, 25 study French and Russian, 15 study Russian and German and 8 study
all three languages.
Find the number of students who study at least one of the three languages.
(5 Marks)
b) A man, woman, boy, girl, dog and cat are walking down a long and winding road
one after the other.
i) In how many ways can this happen? (2 Marks)
ii) In how many ways can this happen if the dog comes first. (3 Marks)
(5 Marks)
d) Determine the validity of the following argument:
If my brother passes the CPA exams in the first attempt, l will give him a valuable
prize. Either he passes the exams or l was out of the country. I did not give my
brother a prize this time although he passed the exam. Therefore, l was out of the
country. (5 Marks)
QUESTION TWO
a) Let
p q
be “If it rains, then l get wet”. Write down the inverse, converse and
contrapositive of this proposition. (6 Marks)
b) Write the negation of the following statements:
i) He swims if and only if the water is warm.
ii) Kenya will be prosperous if and if its citizens are industrious.
iii) If it is cold , then he wears a coat but no sweater. (6 Marks)
c) Construct the truth table for
QUESTION THREE
a) Find the smallest positive integer x such that when x is divided by 3 it yields a
remainder 2, when x is divided by 7 it yields a remainder 4, and when x is divided
by 10 it yields a remainder 6. (8 Marks)
QUESTION FOUR
a) Define a Boolean Algebra. (5 Marks)
b) Write the dual of each Boolean equation:
(5 Marks)
d) Test the validity of the following argument: If the rainfall is good, the yield of
crops is good. The yield of crops was not good. Therefore the rainfall was not
good. (6 Marks)
QUESTION FIVE
a) Draw the graph K2,5. (5 Marks)
b) Which connected graphs can be both regular and bipartite? (5 Marks)
c) Of a group of 20 persons, 10 are interested in music, 7 are interested in
photography and 4 like swimming; further more 4 are interested in both music
and photography, 3 are interested in both music and swimming, 2 are interested in
both photography and swimming and one is interested in music, photography and
swimming. How many are interested in photography but not in music and
swimming? (5 Marks)
