The University of Sydney
School of Mathematics and Statistics
Assignment
MATH1004: Discrete Mathematics
Semester 2, 2015
Lecturers: Anne Thomas and Stephan Tillmann
Instructions to students:
This assignment counts for 5% of your overall assessment for MAT
8004A Semester 2 2012
Page 10 of 20
Extended Answer Section
There are three questions in this section, each with a number of parts. Write your answers
in the space provided below each part. If you need more space there are extra pages at the
end of the ex
MATH1004
Summer School, 2015
Discrete Mathematics
Solutions to Assignment 3
1. Let A = cfw_1, 2, . . . , m and B = cfw_1, 2, . . . , n for some m, n 1. Let X be the set of all
functions from A to B. Our goal is to nd a formula for the number of surjective
MATH1004
Summer School, 2015
Discrete Mathematics
Solutions to Assignment 1
This assignment is due by the end of the 4pm lecture on Wednesday 14 January 2014.
A cover sheet must be signed and attached, and can be downloaded from
http:/www.maths.usyd.edu.a
6.9174015
deacon: 4!
SIT 90%
K e S x ’3 OM demuﬁ (7&5
X QC S K /3 53f au zfemonL 0,0,3
59-7- 5/3"L $0994+¢72T
5 2 T TISF a JUGS/0‘ 412.3
(5 (5 0K JbtheJL 727‘
5 z T 53 7‘ 0W4 7— g 3
/N = .99" of Q/ kqv‘uml MUMSQN ’~ {0‘
T HE U NIVERSITY OF S YDNEY
S CHOOL OF M ATHEMATICS AND S TATISTICS
Problem Set 1
MATH1004: Discrete Mathematics
1.
Semester 2, 2015
(a) Which of the following strings of brackets are balanced? In each case, explain
carefully why the string is, or is not,
T HE U NIVERSITY OF S YDNEY
S CHOOL OF M ATHEMATICS AND S TATISTICS
Solutions to Exercises for the Tutorial in Week 3
MATH1004: Discrete Mathematics
Semester 2, 2015
1. Let A = cfw_1, 2, 3, cfw_2, cfw_2, 3, 4. Which of the following statements are true?
(
MATH1004
Summer School, 2015
Discrete Mathematics
Tutorial 1
1. The rst few rows of Pascals triangle are written down below. Recall that each entry is
equal to the sum of the two numbers immediately above it.
n = 0:
1
n = 1:
1
n = 2:
1
n = 3:
n = 4:
1
1
1
MATH1004
Discrete Mathematics
Summer School, 2015
Solutions to Assignment 2
This assignment is due by the start of the 2pm lecture on Friday 24 January 2014. A
cover sheet must be signed and attached, and can be downloaded from
http:/www.maths.usyd.edu.au
MATH1004
Summer School, 2015
Discrete Mathematics
Solutions to Assignment 5
This assignment is due by the end of lectures on Wednesday 11 February 2015. A cover
sheet must be signed and attached, and can be downloaded from
http:/www.maths.usyd.edu.au/u/UG
8004A Semester 2 2010
Page 10 of 17
Extended Answer Section
There are three questions in this section, each with a number of parts. Write your answers
in the space provided below each part. If you need more space there are extra pages at the
end of the ex
MATH1004
Summer School, 2015
Discrete Mathematics
Solutions to Assignment 4
This assignment is due by the end of class on Friday 6 February 2015. You may submit
this assignment by email at any point before the due time. A cover sheet must be signed and
at
8004A Semester 2 2011
Page 10 of 16
Extended Answer Section
There are three questions in this section, each with a number of parts. Write your answers
in the space provided below each part. If you need more space there are extra pages at the
end of the ex
mp0,: 5 ' 12W?- 201!
[(511M {0 ago-e /ocf fae [ﬁvsﬂ We -— her: r1; au aﬂfrcvxr'méwﬂi
Q2 Morgaé‘J hum A, K .9 K. Them
m X\(Au8) = (Sm/«3 n (WAR)
(23 X\(An73\ 2 (PR/SC) U (K\73)
(a. Pick;ch [ii-f a Prat? (ff) .'
K\$u73\