UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE DEGREE OF BACHELOR OF
BCU 102 FOUNDATIONS OF MATHEMATICS
DATE: AUGUST, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.
QUESTION ONE [30 MARKS]
(a) Perform the indicated operations on
(b) In a recent survey of400
students in a school,100
were listed as smokers and150
as chewers of gum;75
were listed as both smokers and chewers. Find how many students
are neither smokers nor gum chewers.
d) Construct the truth table value for the compound formula.
e) In each of the following sentences, determine which, is a statement or not.
i. Every rectangle is a square.
ii. The sum of three angles of a triangle is 0
iii. How are you?
QUESTION TWO [20 MARKS]
a) In survey of30students, it was found that19take Mathematics,17take Music ,11take History,7
take Mathematics and History,12take Mathematics and Music,5takeMusic and History and2
take all three courses. Find
i. Draw a Venn diagram to represent the above information. [4 Marks]
ii. The number of students that take Mathematics but do not take History [2 Marks]
iii. The number of students that take exactly two of the three subjects. [2 Marks]
iv. The number of students that take at least one of the three subjects. [2 Marks]
b) Prove that the following argument is valid.
‘If he works hard, he will be successful. He was successful. Therefore, he did not work hard.’
QUESTION THREE [20 MARKS]
a) Define the following terms as used in logics.
i. Proposition [1 Mark]
ii. Statement variables [1 Mark]
iii. Truth value [1 Mark]
b) In each of the following, translate the given compound statement into a symbolic form.
i. It is not true that I am not friendly to you.
ii. The sky is blue and grass is green.
iii. Ashok reads Indian Express or Statesman.
iv. If it rains then we will not go to school.
v. He will be successful if and only if he works hard.