August 2000
MA214 : DISCRETE MATHEMATICS

QUESTION 3

Total Marks: 15 Marks

• Question 1
• Question 2
• Question 4
• Question 5
• Cover Page

SUGGESTED SOLUTIONS
Solutions and allocated marks are indicated in green.
Return to Question 3

(a) Consider the following argument:
If the workers are well paid, then the project will be finished on time. If the
project is not finished on time, then the boss will be sacked. The boss is not
sacked, therefore the workers are well paid.
Defining w, p, b as follows:
w -the workers are well paid;
p -the project is finished on time;
b- the boss is sacked,
construct a truth table to determine whether or not this argument is valid. [8]

2 marks for considering all combinations of w, p and b. Deduct one mark
for each omission or error.
Argument is not valid because not all entries in far right hand column are
true. [1]

(b) Show, using Venn diagrams, that the sets (A-B)(C-B) and
((AC)-B)B' are equal. Show your working clearly. [7]