MASSEY UNIVERSITY
Institute of Fundamental Sciences
Mathematics
160.212 Discrete Mathematics
Distance and Internal
Assignment 2
Semester One, 2015
1. Let be the relation dened on R2 by
(x, y) (z, w)
x + y z + w.
So for example (2, 3) (1, 7), because 2 + 3

123.103 Introductory Chemistry, Organic Chemistry, Assignment #3
Shapes of Organic Molecules
In this assignment you will combine your knowledge of functional groups and
molecular shapes/Lewis diagrams to answer the questions below. Use skeletal
structures

STAGE 3: Developing your solution
In order for your industry to thrive in 2070 it must adapt to future challenges. Now that you
understand the industry and have identified what these future challenges might be you now
need to come up with some solutions.

123.103 Introductory Chemistry, Molecules and Intermolecular Forces, Assignment #2
Investigating Molecules and Forces between
Molecules
This assignment will build on your knowledge of chemical bonding, the shapes of molecules
and forces between molecules.

After completing the future challenges there were two very clear issues that may cause
problems for the deer industry in the next 100 years, these were the increase in vegetarianism
and veganism and more people becoming interested in meat-free diets. The

Assignment 1
Study SG1 Chapters 0, 1 and 2
[100 marks total]
1.
2.
3.
4.
Let
f (x) =
x+2
.
x3
(a)
If possible find the values of f (3), f (2), f (0), f (1), f (3). Some of these may be
undefined.
(b)
What is the domain of f ? Give your answer using interv

Total Work Rate of Breathing Optimization in Co2
Inhalation and Exercise
YAMASHIRO, S. M., J. A. DAUBENSPECK, T. N. EAURITSEN, AND F. S. GRODINS.
J. Appl. Physiol. 38(4): 702-709. 1975.-
The hypothesis that respiratory frequency and the relative durations

Terminology and Results
[These will be made available at the test and examination]
1.
Let p, q, r be propositions. Then we have:
de Morgans laws:
~ ( p ! q) " (~ p# ~ q)
~ ( p ! q) " (~ p# ~ q)
commutative laws:
p ! q " q ! p and p # q " q # p
distributiv

MASSEY UNIVERSITY
Institute of Fundamental Sciences
Mathematics
160.212 Discrete Mathematics
Distance and Internal
Assignment 1 Solutions
Semester One, 2015
1. Are the expressions
(p q) r
and
p (q r)
logically equivalent? Answer the question two ways: rst

MASSEY UNIVERSITY
Institute of Fundamental Sciences
Mathematics
160.212 Discrete Mathematics
Distance and Internal
Assignment 3
Semester One, 2015
1. Find the greatest common divisor (gcd) of 693 and 399, using the Euclidean algorithm.
Hence express d = g

MASSEY UNIVERSITY
Institute of Fundamental Sciences
Mathematics
160.212 Discrete Mathematics
Distance and Internal
Assignment 1
Semester One, 2015
1. Are the expressions
(p q) r
and
p (q r)
logically equivalent? Answer the question two ways: rst using a t

MASSEY UNIVERSITY
Institute of Fundamental Sciences
Mathematics
160.212 Discrete Mathematics
Distance and Internal
Assignment 4
Semester One, 2015
Note: For all problems make sure to justify your ndings by giving
reasons, a proof or a counter-example, as

123.103 Introductory Chemistry, Atoms and the Periodic Table, Assignment #1
Flames and Lights
Your assignment is to analyse some of the common sources of light around the home.
You will carry out some flame tests and then make a piece of apparatus to expl