AST21111
Discrete Mathematics
2. Logic II
1
Conditional Statements
Given propositions p and q, the compound proposition
p q is called the conditional statement. p is called the
antecedent ( ) and q is called the consequent ( ).
p q is read p implies q.
e.
CGE 13204
Food and
Health
Unit 1: Overview and
nutrition
About the lecturer
Name: Dr Christy Lau C. C.
Consultation Hour:
17:00-18:00 on Every Monday at CityU campus
16:00-17:00 on Every Tuesday at Telford Annex
By appointments on Thursday and Friday at
C
AST21111
Discrete Mathematics
3. Methods of Mathematical
Proof and Elementary Number
Theory
1
Mathematical Proofs
A mathematical proof is a valid argument that shows the truth
of a mathematical statement is deduced from the truth of
premises in the argume
AST21111
Discrete Mathematics
2. Logic III
1
Predicates
In English grammar, the word predicate refers to the part
of a sentence that gives information about the subject.
In the sentence Vincent Kwan is a teacher at CCCU. The
words Vincent Kwan is the subj
AST21111
Discrete Mathematics
2. Logic I
1
Propositions
Mathematics involves mathematical propositions.
A proposition ( ) is a sentence that is either true or false but
not both.
e.g.
Vincent Kwan is a teacher. is a proposition as it is truth-bearing.
Wha
MA1300
Problem Set # 14, Solutions
1. Determine whether the series converges or diverges.
X
n+1
,
(a).
n n
n=1
(b).
X
(2k 1)(k2 1)
k=1
(k + 1)(k2 + 4)2
,
X
4n+1
(c).
.
3n 2
n=1
n+1
P 1
P
n+1
have positive terms. Since limn n 1 n = 1 and
and
Solution. (
MA1300
Problem Set # 1, Solutions
1. Find the domain and sketch the graph of the function.
G(x) =
Solution:
3x + |x|
x
When x = 0, G(x) has no definition; when x 6= 0, G(x) is well defined. So the domain of G is
(, 0) (0, ). The sketch of G is
y
4
y = G(x
MA1300
Problem Set # 3, Solutions
1. Use the definition of continuity and the properties of limits to show that the function is continuous
at the given number a.
a = 4.
f (x) = x2 + 7 x,
2
2t 3t
,
a = 1.
(2)
f (t) =
1 + t3
Proof. (1), since limx4 7 x = 3
MA1300
Problem Set # 3
1. (P91, #1.8.12, 1.8.14) Use the definition of continuity and the properties of limits to show that the
function is continuous at the given number a.
a = 4.
f (x) = x2 + 7 x,
2
2t 3t
f (t) =
,
a = 1.
1 + t3
(1)
(2)
2. (P91, #1.8.15
MA1300
Problem Set # 13, Solutions
1. Determine whether the sequence converges or diverges. If it converges, find the limit.
3 + 5n2
,
n + n2
r
n+1
(b). an =
.
9n + 1
(a). an =
Solution:
(a). We have
3
+5
n2
1
n
n +1
lim an = lim
n
= 5,
so cfw_an is conv
MA1300
Problem Set # 4, Solutions
1. Find the values of a and b that make f continuous everywhere.
2
x 4
if x < 2
x2
f (x) =
2
ax bx + 3 if 2 x < 3
2x a + b
if x 3.
Solution. For making f continuous everywhere, sufficient and necessary conditions are
2
EAP Writing Assessment Descriptors: Assessment 2
TASK FULFILMENT
(25%)
5
Organisation is clear, logical and effective at all Uses a wide range of sentence structures
levels
correctly and appropriately
An effective thesis is established and strongly
argu
Pre-reading discussion
1. In small groups, discuss the following:
What do you know about GM foods?
What benefits and risks might be
linked to genetically-modified foods?
List 3 points each.
2. Watch a short video and take
notes. Is the video pro or a
Pre-reading activities
Vocabulary focus
Collocation and word form
Feedback on practice writing
In groups of 3/4, speculate on
how long the average person
lives.
Discuss:
Factors that affect a persons
longevity. Use the table on p.137
Factors
Diet
Positive
EL0200
We e k 8
Complex Noun Phrases & Hedging
Unit 4 - Task 5: A few more grammar concepts
Most common sentence type in English: A subject and a verb (s+v)
Exception: Imperatives Stop! / Please sit down.
A subject in a sentence:
1. Can be a single wor
More on citation formats & practice
Reporting verb patterns
Writing task practice GM Foods
Homework & IL
Use APA citation format (American
Psychological Association)
You can incorporate evidence into
your writing by:
1. Quoting
2. Paraphrasing (& summar
Unit 4 Appendix: More on Complex Noun Phrases
Determiners & pre-modifiers
Various kinds of word can appear before a head noun. These can be divided into
two main types: determiners and pre-modifiers.
Determiners include various types:
Determiner
type
Exam
Unit 6 Reading Comprehension (pp.108)
A
Multiple choice:
1.B/ 2.D/ 3.A/ 4.D/ 5.A
B
For and Against
1.
2.
3.
4.
5.
6.
genetic
allergic
pesticides
slip by undiscovered
adequately tested
a public relations exercise
Vocab Practice A: completion
1.
2.
3.
4.
5.
EE3015 Tutorial 9 (Transport Layer)
Review Questions: Describe why an application developer might choose to run an application over UDP rather than TCP.
Problems: 1. Suppose Host A sends two TCP segments back to back to Host B over a TCP connection. The f
EE3015 Tutorial 8
(IP address, IP fragmentation, NAT) Review Questions Do routers have IP addresses? If so, how many? What is the difference between routing and forwarding? What is the 32-bit binary equivalent of the IP address 223.1.3.27?
Problems: 1. Co
EE3015 Tutorial 7
(WiFi, VC network and datagram network) Problems: 1. What does it mean for a wireless network to be operating in infrastructure mode? If the network is not in infrastructure mode, what mode of operation is it in, and what is the differen
EE3015 Tutorial 6
(Ethernet and Ethernet Switch)
Problems 1. Suppose nodes A and B are on the same 10 Mbps Ethernet segment, and the propagation delay between the two nodes is 225 bit times. Suppose node A begins transmitting a frame and before it finishe
EE3015 Tutorial 5 (Medium Access Control)
1.
Suppose that the pure ALOHA protocol is used to share a 56 kbps satellite channel, and that frames are 2000 bits long. Find the maximum throughput of the system in frames/second. (Note: the throughput of pure A
EE3015 Tutorial 4
(Go-Back-N and Selective Repeat) Problems: 1. Two hosts communicate with each other using a pipelined protocol with window size equal to w. Let the transmission rate of the link connecting the two hosts be 10 Mbps and the end-to-end dela
EE3015 Tutorial 3
(Data Communications) Review Questions Describe what pulse coded modulation is. What is the difference between multimode step-index fiber and multimode graded-index fiber? Problems 1. An audio digitizing utility in a PC samples an input
EE3015 Tutorial 2
(Delay and Protocol Layering) Review Questions What are the seven layers in the OSI model? What are the five layers in the Internet protocol model? What are the four most important types of delay in a computer network? Problems 1. Consid
EE3015 Tutorial 1
(Circuit Switching vs. Packet Switching; Throughput and Delay) Review Questions: What are the three major components of the Internet? What is the difference between circuit switching and packet switching? What is multiplexing? List some