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