Paper Code: 715189
Algebra and Discrete Mathematics
Lecturer: Ji Ruan
Assignment 2
Due 4:30pm Friday 18 September 2015
Name .
Question
1
ID number.
Marks Possible
10
2
24
3
24
4
18
5
24
Total
100
6 Bonus
Marks Given
10
Instructions:
Please attach this she
715189 Algebra and Discrete Mathematics Final Examination
Student ID:
Semester 2, 2014
Model Answers
1. Let A i = cfw_x Z| i x i for integer i N. (Note that 0 N)
Find
(a) A 0 A 1 by enumeration.
(2 marks)
Model Answer:
A 0 A 1 = cfw_(0, 1), (0, 0), (0,
715189 Algebra and Discrete Mathematics
Model Answers for Assignment 1
Question 1 (10 marks) Using Euclids algorithm, determine if the following rational numbers are in reduced form. If not, write down their reduced forms. Show your working.
1.
179
78
Mod
Student ID:
Number of additional sheets:
715189 Algebra and Discrete Mathematics
Semester 2, 2015
Mid-term Test
August, 2015
Time Allowed 55 minutes (plus 5 minutes reading time).
Instructions
This is a closed-book test.
Please answer all questions and
Student ID:
Number of additional sheets:
715189 Algebra and Discrete Mathematics
Semester 1, 2015
Final Examination
June 2015
Time Allowed Two hours (plus reading time).
Instructions
This is a closed-book exam.
Please answer all questions in the space p
ADM 715189, 2015, semester 2
Mock Exam
Question 1 A = cfw_a, b, c, B = cfw_c, d, e, f . Find the cardinalities:
1) |A B|,
2) |A B|,
3) |A15 |,
4) |P (B)|.
Question 2 Function f : Z Z Z is given by: f (x, y) = xy + 2.
1) Is the function f one-to-one/1-1 ?
715189 ALGEBRA AND DISCRETE MATH
AUCKLAND UNIVERSITY OF TECHNOLOGY 2015
TUTORIAL WEEK 1
Question 1. I am thinking of one of these five cards:
You have to try to find out which one I am thinking of. Some clues:
The value of my card is a prime number.
The
MATH502 Algebra and Discrete Mathematics
Tutorial - ANSWERS
Week 9
1. Find a parametric & nonparametric linear equation passing two points, P and Q.
(a) P = (1, 0) and Q = (3, 5)
(b) P = (1, 1) and Q = (2, 3)
(c) P = (1, 2) and Q = (0, 4)
(d) P = (1/2, 1)
MATH502 ALGEBRA AND DISCRETE MATHEMATICS (ADM)
TUTORIAL WEEK 2
AUCKLAND UNIVERSITY OF TECHNOLOGY
2016
Question 1. Describe the following sets, using both comprehension and enumeration. The universal set
is N.
(a) The set of all even numbers from 2 to 12 i
MATH502 ALGEBRA AND DISCRETE MATHEMATICS (ADM)
TUTORIAL WEEK 3
AUCKLAND UNIVERSITY OF TECHNOLOGY
2016
Question 1. Use set operation laws (attached in last page) to show the following set equality. Clearly
indicate which law you use in each step.
a) A (A B
MATH502 ALGEBRA AND DISCRETE MATHEMATICS (ADM)
TUTORIAL WEEK 4
AUCKLAND UNIVERSITY OF TECHNOLOGY
2016
Question 1. Given relation C = cfw_(x, y) Z2 | x y is even
(a) Show that C is an equivalence relation.
(b) Show the following equivalence classes of C by
MATH502 Algebra and Discrete Mathematics
Tutorial
Week 8 - ANSWER
1. (a) A 16 team bowling league has $8000 to be awarded as prize money.
If the last-place team is awarded $275 in prize money and the award
increases by the same amount for each successive
MATH502 ALGEBRA AND DISCRETE MATHEMATICS (ADM)
TUTORIAL WEEK 1
AUCKLAND UNIVERSITY OF TECHNOLOGY
2016
Question 1. I am thinking of one of these five cards:
You have to try to find out which one I am thinking of. Some clues:
The value of my card is a prim
MATH502 ALGEBRA AND DISCRETE MATHEMATICS (ADM)
TUTORIAL WEEK 5
AUCKLAND UNIVERSITY OF TECHNOLOGY
2016
Question 1. Given the set of propositions cfw_p, q, r, s, decide if any of the following is a well-formed
formula:
(1) (p q) (qq)p)
(2) (p q) r
(3) (p (q
MATH502 Algebra and Discrete Mathematics
Tutorial
Week 10 - ANSWER
1. Solve the following questions.
(a) A store owner purchased 20 independent light bulbs and 30 fluorescent bulbs for a total cost of
$40. A second purchase, at the same prices, included 3
MATH502 ALGEBRA AND DISCRETE MATHEMATICS (ADM)
TUTORIAL WEEK 6
AUCKLAND UNIVERSITY OF TECHNOLOGY
2016
Question 1. First give the contraposition of the following statements, then prove them by contraposition:
(1) Suppose x Z. If x2 6x + 5 is even, then x i