MAT1830 - Discrete Mathematics for Computer Science
Assignment #4
To be handed in at the beginning of your support class in week 6 (1317 April)
Show your working for all questions.
(1) Prove by induction that, for all integers n 1,
1 + 4 + 7 + + (3n 2) =
Housekeeping
Assignment Solutions 1 are now available.
Assignment 2 is due at the beginning of your support class this week.
Assignment 3 is available and is due at the beginning of your support
class in week 5 (30 Mar2 April).
Tutorial sheet 3 and tutori
Housekeeping
Assignment 2 is due at the beginning of your support class in week 4
(2327 March).
Assignment 3 is now available and is due at the beginning of your
support class in week 5 (30 Mar2 April).
Tutorial solutions 2 are now available.
Assignment s
Housekeeping
Assignment 1 is due at the beginning of your support class THIS WEEK.
Assignment 2 is now available and is due at the beginning of your
support class in week 4 (2327 March).
Tutorial sheet 3 is now available.
MAT1830
Lecture 8: Predicate logi
Housekeeping
Assignment 1 is due at the beginning of your support class THIS WEEK.
Assignment 2 is now available and is due at the beginning of your
support class in week 4 (2327 March).
Tutorial sheet 2 and tutorial solutions 1 are also now available.
MA
MAT1830 - Discrete Mathematics for Computer Science
Assignment #5
To be handed in at the beginning of your support class in week 7 (20 24 April)
Show your working for all questions.
1. Let a(x) : cfw_8, 9, 10, 11, 12, 13, 14, 15, 16 N be the function dene
MAT1830 - Discrete Mathematics for Computer Science
Assignment #6
To be handed in at the beginning of your support class in week 8 (27 April 1 May)
Show your working for all questions.
1. For each of the binary relations E, F and G on the set cfw_a, b, c,
MAT1830 - Discrete Mathematics for Computer Science
Assignment #7
To be handed in at the beginning of your support class in week 9 (4 8 May)
1. Write down the rst ve values of each of the following recursive sequences.
(a) r0 = 2,
rn = (rn1 )2 5
(b) s0 =
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #1
Show your working for all questions.
1. Are the following statements true or false?
(a) 14 20 (mod 8)
(b) 4 divides 16
(c) 11 2 (mod 3)
(d) 9 is prime
(e) 1000 12544 (mod 5)
(f) 66 divi
Questions.
1. Use the Euclidean algorithm to show that gcd(269, 42) = 1.
2. Use the Euclidean algorithm to nd a multiple of 269 and a multiple of 42 that dier by 1.
Solutions.
1.
269
42
17
8
=
=
=
=
6
2
2
8
42
17
8
1
+
+
+
+
17
8
1
0
(1)
(2)
(3)
(4)
So gc
MAT1830 - Discrete Mathematics for Computer Science
Assignment #8
To be handed in at the beginning of your support class in week 10 (11 15 May)
Show your working for all questions.
1. Let s0 , s1 , s2 , . . . be a recursive sequence defined by
s0 = 4, s1
MAT1830 Sample Exam 2
(1) (a) Use the Euclidean algorithm to find the greatest common divisor of 633 and 255.
[5]
(b) Find integers x and y such that 633x + 255y = 6, or explain why none exist.
[4]
(c) Is there an integer z such that 255z 7 (mod 633)? If
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MAT1830 - Discrete Mathematics for Computer Science
Assignment #1
To be handed in at the beginning of your support class in week 3 (1620 March)
Show your working for all questions.
1. (a) Use the Euclidean algorithm to nd the greatest common divisor of 10
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #3 and Additional Practice Questions
If youre missing out on your usual support class on Fri 25 Mar, you are welcome to attend any other support
class in week 4 (times will be posted on mo
MAT1830 - Discrete Mathematics for Computer Science
Tutorial Sheet #2 and Additional Practice Questions
Tutorial Questions
1. (a) Draw a truth table for the proposition (b p) (b p) b.
(b) Is it a tautology, a contradiction or neither?
(c) Give your own ex
MONASH UNIVERSITY
SCHOOL OF MATHEMATICAL SCIENCES
MAT2003 Continuous Mathematics for Computer Science
Mathematics Laboratory 6
(Week 7)
SOLUTIONS
As part of answering all lab questions in this unit, give reasons and mathematical proofs or
arguments for ho
MAT1830 - Discrete Mathematics for Computer Science
Assignment #8 Solutions
1. Let S be the event that Bond survives.
Let M be the event that a male scorpion bit Bond.
[1]
(Because Bond was bitten by either a male or female scorpion, M is the event that B
MAT1830 - Discrete Mathematics for Computer Science
Assignment #1 Solutions
1. (a) True (because 3 5 = 15).
[1]
(b) False (because 5 does not divide 13 24 = 11).
[1]
(c) False (because there is no integer k such that 10k = 2).
[1]
(d) False (for example g
MAT1830 - Discrete Mathematics for Computer Science
Assignment #2 Solutions
1.
p
T
T
F
F
q
T
F
T
F
pq
T
F
T
T
(p q)
F
T
F
F
p (p q)
F
T
F
F
(p (p q)
T
F
T
T
So this is a not tautology (because the final column in the truth table contains an F).
2.
a
T
T
T
MAT1830 - Discrete Mathematics for Computer Science
Assignment #3
To be handed in at the beginning of your support class in week 5 (4 8 Apr)
Show your working for all questions.
(1) Let P (x, y) be the predicate y = 2x. Consider the statements
(a) xyP (x,
MAT1830 - Discrete Mathematics for Computer Science
Assignment #3
To be handed in at the beginning of your support class in week 5 (30 Mar 2 Apr)
Those missing out on support classes on Fri 3 Apr may attend any other support class in that week and
submit
MAT1830 - Discrete Mathematics for Computer Science
Assignment #6 Solutions
1. E is reflexive and symmetric and transitive.
E is not antisymmetric (for example, aEb and bEa).
F is reflexive and antisymmetric and transitive.
F is not symmetric (for example
MAT1830 - Discrete Mathematics for Computer Science
Assignment #9 Solutions
1. Let X be the number of heads flipped. Then X is a binomial random variable with p =
and n = 100.
Using the formula for the binomial distribution with p =
Pr(X = 1) =
100 3 65
MAT1830 - Discrete Mathematics for Computer Science
Assignment #7 Solutions
1. (a) A ternary string of length 10 is an ordered selection of 10 elements from the set cfw_0, 1, 2 with
3 elements. There are 310 such selections.
[1]
(b) Such a string is a per