August 1997
MA214: DISCRETE MATHEMATICS

QUESTION 1 (Compulsory)

Total Marks: 20 Marks

 Click here to access other questions

Click to access
SUGGESTED SOLUTIONS
for Question 1
1. (a) (i) What is the contrapositive of the following statement? [2]
" If n is divisible by 6, then n is divisible by 2 and n is divisible by 3."
(ii) What is the negation of the following statement? [3]
" A is a subset of B and B is a subset of C."
(b) (i) Define the relation that holds between two integers a and b if and only if a divides b with no remainder. [1]
(ii) Define what it means for this relation to be transitive. [1]
(iii) Prove that this relation is transitive. [4]
(c) Suppose that a graph has five vertices whose degrees are 0, 2, 2, 3 and 9. How many edges does the graph have? [2]
(d) Use Venn diagrams to show the following relationships.
(i) All human beings are mortal. Zeus is not mortal. [2]
(ii) The set of real number Â, the set of rational numbers Q, and the set of integers Z. [2]
(e) A batch of 100 students' test papers were each marked by two markers, A and B. Marker A obtained the statistics: mean = 65, interquartile range = 30, and standard deviation = 5. If marker B is stricter, such that each student obtains three marks fewer than those awarded by A, what will B's statistics be?
(i) mean [1]
(ii) interquartile range [1]
(iii) standard deviation [1]