DMTH137 Assignment 1, Solutions
Logic, Sets, Relations, Graphs
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Due 1:00 pm. Monday 5 September
Logic & Predicates, Sets, Relations
1. (a)
p q p q p q q (p q)
(i) Construct the truth table for q (p q) .
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DMTH137 Assignment 2, Solutions
Graph Algorithms, Counting Techniques
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Due 5:00 pm. Monday 10 October
Graph Algorithms
1. Explain why a simple graph G = (V, E) has no Eulerian walk,
where the vertices are V = cfw

What is the total weight of the minimal spanning tree?
Functions and Counting Techniques
4.
Let f : Z12 Z12 : x 9x + 1 where arithmetic is done modulo 12.
(a) Show that f is neither injective, nor surjective.
(b) Now consider g, where g : Z12 Z12: x 7x +

Vectors and Matrices graphics programming
The ability to create computer graphics that change with a parameter is very important, not just for Mathematics,
Scientific Visualisation, Computer Games, but also for all kinds of electronic documentation and ad

(b) In the following Venn diagrams, note how the shaded regions would remain the same if the locations of sets B
and C were interchanged. Write down expressions for each of the shaded regions, where the expressions also
display this symmetry between B and