# BIT 1206  DISCRETE MATHEMATICS .

UNIVERSITY EXAMINATIONS 2017/2018
ORDINARY EXAMINATION FOR BACHELOR OF SCIENCE
INFORMATION TECHNOLOGY – APPLIED COMPUTING
BIT 1206 DISCRETE MATHEMATICS (DAY/EVENING)
DATE: DECEMBER, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and Any other TWO questions

QUESTION ONE
(a) Let + and ∗ be operations in B = 0,1 defined in Fig 1 below. Suppose that the
compliments are defined by I = 0 and 0 ꞌ

= 1 show that B = 0,1 is a Boolean algebra

Find
(i) A∪B
(3 Marks) (ii) B∪C
(3 Marks)
Total [30 Marks]
QUESTION TWO
a) Define the following terms
(i) one-to-one (or injective ) Function (2 Marks)
(ii) Onto (or surjective) Function (1 Mark)
(iii) one-to-one correspondence (or bijective) Function (2 Marks)
(iv) Invertible Function (2 Marks)
(b) Let A= a,b,c,d,e and B be the set of letters in the alphabet. Let the functions f and g and
h
from A into B be defined as follows

(i) Is gof defined ? if so what is the domain and codomain ? (2 Marks)
(ii) Is hof defined? if so what is the domain and codomain ? (2 Marks)
(iii) Is FohoG defined ? if so what is the domain and codomain ? (2 Marks)
(iv) Is GoFoh defined ? if so what is the domain and codomain ? (2 Marks)
Total[20 Marks]
QUESTION THREE
(a) Define the following terms as used in graph theory
(i) A path (2 Marks)
(ii) A simple path (2 Marks)
(iii) A closed path (2 Marks)
(b) Draw a diagram for each of the following graphs

QUESTION FOUR
(a) List the elements of the following sets

(d) A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see
which of the three popular options, air-conditioning (A), radio (R), and power windows (W) were
5 had air-conditioning and Power windows
3 had all the three options
Find the number of cars that had
(i)Only power windows (2 Marks)
(ii) Only air-conditioning (1 Mark)
(iv) radio and power windows but not air – conditioning (1 Mark)
(v) air conditioning and radio but not power windows (1 Mark)
(vi) Only one of the options (2 Marks)
Total [20 Marks]
QUESTION FIVE
(a) Test the validity of the following argument:
S1 : If two sides of a triangle are equal, then the opposite angles are equal.
S2 : Two sides of a triangle are not equal
S: The opposite angles are not equal. (4 Marks)
(b) Determine the truth values of each statement
(i) 2 + 2 = 4 iff 3+6 = 9
(ii) 2+ 2 = 7 if and only if 5 + 1 = 2
(iii) 1 + 1 = 2 iff 3 + 2 = 8
(iv) 1 + 2 = 5 if and only if 3+ 1 = 4 (4 Marks)
(c) Use the Laws of algebra of propositions to prove the following

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