PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
PAN AFRICA CHRISTIAN UNIVERSITY
DIPLOMA IN INFORMATION AND COMMUNICATION TECHNOLOGY
END OF TERM EXAMINATION
DEPARTMENT:
COMPUTING AND INFORMATION TECHNOLOGY
COURSE CODE:
DICT0114
CAMPUS:
ROYSAMBU
COURSE TITLE:
FOUNDATION MATHEMATICS
EXAM DATE:
TUESDAY, 6TH DECEMBER 2016
TIME:
14:00 – 17:00 HRS
INSTRUCTIONS

This exam script has TWO (2) sections.

Read all questions carefully before attempting.

Answer All questions in Section A and any other Four questions in Section B.

Write your student number on the answer booklet provided.
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PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
SECTION A
(Answer ALL questions in this section)
Question 1:
a) Convert the following:
i) 11.110112 to decimal equivalent
(6 Marks)
ii) 7.562510 to binary number
iii) AD3B16 to octal equivalent
b) Determine the power set P(A) of A = {1, 2, 3, 4}.
(2 Marks)
c) Consider the universal set U = {1, 2, 3, …, 8, 9} and sets A = {1, 2, 5, 6}, B = {2, 5,
7}, C = {1, 3, 5, 7, 9}.
Find:
i) A ∩ B
ii) A ∪ C) \ B
d) A die is rolled, find the probability that an even number is obtained.
(2 Marks)
(2 Marks)
(2 Marks)
e) A farmer buys 3 cows, 2 pigs, and 4 hens from a man who has 6 cows, 5 pigs, and 8
hens. Find the number m of choices that the farmer has.
f) Find the determinant of matrix B:
(3 Marks)
(3 Marks)
SECTION B
(Answer any FOUR (4) questions in this section)
Question 2:
a) Let U = {1,2, …, 9} be the universal set, and let
A = {1, 2, 3, 4, 5},
C= {5, 6, 7, 8, 9},
E= {2, 4, 6, 8},
B = {4, 5, 6, 7},
D= {1, 3, 5, 7, 9},
F = {1, 5, 9}.
Find:
i) A U B
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(2 Marks)
PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
ii) (B∩F) ∪ (C∩E)
(2 Marks)
iii) D/E
(2 Marks)
iv) (A/C)C
(2 Marks)
v) A ∩ (D U F)
(2 Marks)
b) Convert the following:
i) 94B16 to decimal equivalent
(10 Marks)
ii) 4910 to binary number
iii) 258 to decimal equivalent
iv) 111011002 to octal equivalent
v) AC2716 to binary number
Question 3:
a) Define the following terms:
(4 Marks)
i) Set
ii) Disjoint set
iii) Universal set
iv) Empty set
b) Find the Cartesian product of the following sets:
(4 Marks)
A={1,2,3,4} B={a,b,c}
c) Prove the following laws:
i) DeMorgan’s laws; (A ∪ B)C = AC ∩ BC
ii) Distributive Law; A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Question 4:
a) Compute the following:
i) 8!
ii)12P4
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(6 Marks)
(6 Marks)
(6 Marks)
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EXAMINATIONS PAPER
iii)8
C4
b) Determine the number of all the rearrangements in the letters of PARRAMATTA.
(2 Marks)
c) Suppose a bookcase shelf has 5 History texts, 3 Sociology texts, 6 Anthropology
texts, and 4 Psychology texts. Find the number n of ways a student can choose:
i) One of the texts
(3 Marks)
ii) One of each type of text.
(4 Marks)
d)
(5 Marks)
Question 5:
a) Construct the truth table of ￢p ∧ q.
(5 Marks)
b) Verify that the proposition p V￢(p ∧q) is a tautology.
(5 Marks)
c) Show that the propositions ￢(p ∧ q) and ￢p ∨￢q are logically equivalent.
(5 Marks)
d) Let p be “It is cold” and let q be “It is raining”. Give a simple verbal sentence which
describes each of the following statements:
i) ￢p
ii) p ∧ q
iii) p ∨ q
iv) q ∨￢p
(1 Mark)
(1 Mark)
(1 Mark)
(2 Marks)
Question 6:
a) A survey on a sample of 25 new cars being sold at a local auto dealer was conducted
to see which of three popular options, air-conditioning (A), radio (R), and power
windows (W), were already installed. The survey found:
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PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
15 had air-conditioning (A), 12 had radio (R), 11 had power windows (W), 5 had A
and W, 9 had A and R, 4 had R and W, 3 had all three options.
Find the number of cars that had:
i) Only W
(1 Mark)
ii) Only A
(1 Mark)
iii) Only R
(1 Mark)
iv) R and W but not A
v) Only one of the options
(2 Marks)
(5 Marks)
vi) At least one option
(5 Marks)
vii) None of the options
(5 Marks)
Question 7:
a) A pair of dice is rolled. Find the probability of the following event:
i) Sum is equal to 5
ii) 4 appears on the first die
(2 Marks)
(2 Marks)
iii) Sum is less than 13
(3 Marks)
iv) 5 appears on at least one die
(3 Marks)
b)
Find:
i) 3A + 4B
T
ii)A
iii) BA
iv) Inverse of B
(3 Marks)
(1 Mark)
(3 Marks)
(3 Marks)
END
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