# BIT 1206 BAC 1201 BISF 1101 BSD 1202 DISCRETE MATHEMATICS.

UNIVERSITY EXAMINATIONS: 2021/2022
ORDINARY EXAMINATION FOR BACHELOR OFSCIENCE
INFORMATION TECHNOLOGY, BSc. APPLIED COMPUTING, BSD,
BISF
BIT 1206/ BAC 1201/ BISF 1101/ BSD 1202: DISCRETE
MATHEMATICS
(PARTTIME/ DISTANCE LEARNING)
DATE: DECEMBER, 2021 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any Other Two questions

QUESTION ONE
(a)Use the laws of algebra of sets to simplify

[5Marks]
(b)Prove : if π΄ is a subset of the null set π ,then π΄ = π.
[5Marks]
(c)Let π be a subset of π΄ and let β: π β¦ π΄ be an iclusion
map .Show that the inclusion map is one-to-one.
[5Marks]
(d)Find the largest interval π· on which the formulae
π(π₯) = π₯
2
defines a one to one function.
[5Marks]
QUESTION TWO
(a)Find a traversable trail πΌ for the graph πΊ whereπ(πΊ) =
{π΄, π΅, πΆ,π·} and πΈ(πΊ) = [{π΄, πΆ},{π΄,π·},{π΅, πΆ},{π΅,π·},{πΆ,π·}] .
[5Marks]
(b)Draw the multigraph πΊ whose adjacency matrix is

[10Marks]
QUESTION THREE
(a)Determine the number of loops and multiple edges in
a multigraph πΊ from its adjacency matrix

[5Marks]
(b)Let πΊ be a graph with π vertices. Describe two major
drawbacks in the computer storage of πΊ as its adjacency
matrix π΄. [10Marks]
QUESTION FOUR
(a)Prove:There is a path from a vertex π’ to a vertex π£ if and
only if there is a simple path from π’ to π£.
[5Marks]
(b)Consider the statement βif Oscar eats Chinese
food,then he drinks milkβ.
(i)Write the converse of the statement.
[2Marks]
(ii)Write the contrapositive of the statement.
[2Marks]
(c) Consider the function π:{1,2,3,4} β¦ {1,2,3,4} given by

(i) Find π(1)
[1Mark]
(ii) Find an element π in the domain such that π(π) = 1
[1Mark]
(iii) Find an element π of the domain such that π(π) = π
[1Mark]
(iv) Find an element of the condomain that is not in the
range [1Mark]
(d)Consider the function π: β€ β¦ β€ given by π(π) =
{
π + 1: π β ππ£ππ
π β 3: π β π ββ