Exercises for Informal Fallacies
1. We should give an A to Tommy. It is
because if he does not get an A, it is likely
that he will not get enough GPA to be
admitted to HKU. You know, Tommys
parents are quite old and have high
expectation of him.
2. Sinc
1. (K P) v (K Q)
2. P ~K
3. K (P v Q)
4. K
5. ~K
6. ~P
7. (P v Q) K
8. P v Q
9. Q
10. Q v T
/QvT
1. (K P) v (K Q)
2. P ~K
3. K (P v Q)
4. K
5. ~K
6. ~P
7. (P v Q) K
8. P v Q
9. Q
10. Q v T
/QvT
1, Dist
3, Simp
4, DN
2, 5, MT
3, Com
7, Simp
6, 8, DS
9, Ad
Categorical Syllogism Exercise
Identify major, minor, and
middle terms, mood, and figure
All ozone molecules are good absorbers of
UV light.
All ozone molecules are things destroyed by
chlorine.
Therefore, some things destroyed by
chlorine are good abs
There are significant omissions which are necessary in order to render the
Individualists optimism plausible. Either workers and businessmen would
have insurance of various kinds, or they would be insecure in their prosperity.
If they did have the insuran
Vectors
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
7
Algebra
Chapter 7
7.1
7.2
7.3
7.4
7.5
7.6
Vectors
Fundamental Concepts
Addition and Subtraction of Vectors
Scalar Multiplication
Vectors in Three Dimensions
Linear Combination and L
Two Dimensional Co-ordinate Geometry
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
9
Calculus II
9.1
Introduction
9.2
Change of Axes
9.3
Straight Lines
9.4
Equations of Lines Pairs
9.5
Circle
9.6
Parabola
9.7
Ellipse
9.8
Hyperbola
9.1 In
Three Dimensional Co-ordinate Geometry
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
10
Calculus II
Chapter 7
7.8
Chapter 10
Vectors
Vector Equation of a Straight Line
2
Three Dimensional Coordinates Geometry
10.1
Basic Formulas
6
10.2
E
Systems of linear equations
Advanced Level Pure Mathematics
AdvancedLevel PureMathematics
9
Algebra
Chapter 9
Systems of Linear Equations
9.1
2
9.3
Gaussian Elimination
7
9.4
Solutions of Systems of Linear Equations
8
9.5
9.1
Introduction and Existence an
Syllogism
A syllogism is a two-premise deductive
argument.
Or, a categorical syllogism is an argument
in which both the premises and the
conclusion are categorical propositions.
1
There are 3 propositions.
There are 3 terms.
Each term is used twice.
Non
Applications of Definite Integrals
AdvancedLevelPureMathematics
AdvancedLevel P ureMathematics
Applications of Definite Integrals
8
Areas
2
Arc Length
8
Volumes of Solids of Revolution
11
Area of Surface of Revolution
13
Prepared by Mr. K.
Page 1
F. Ngai
Application of Differential Calculus
Date
A-Level Pure Mathematics
Chapter 5 Application of Differential Calculus
Exercise 5A (LHospitals Rule)
Name : _
:
x sin x
x3
1.
Evaluate lim
2.
Evaluate the following limits:
x 0
(a)
3.
1 cos x
x 0
x2
lim
sin nx
x
BASIC CONCEPTS OF
ARGUMENTS
1
What is an Argument?
To justify or defend a claim is to give reasons or
arguments to support it.
Reasoning (or inference) is a psychological
process.
When we express this process into words, we have
arguments.
An argument
Identify Arguments
Use the letters P and C to label
the premises and conclusion of each
argument
Question 1
Titanium combines readily with oxygen,
nitrogen, and hydrogen, all of which have
an adverse effect on its mechanical
properties. As a result, tita
Categorical Logic (I)
1
Categorical Propositions
This logical system was developed by
Aristotle more than 2000 years ago.
Categorical Logic deals with categorical
propositions.
A categorical proposition is a proposition
that relates two categories or c
Identify quantifier, subject,
copula, and predicate
1. No persons who live near airports are
persons who appreciate the noise of jets.
2. Some terrorists are not religious.
1. Quantifier: No
Subject: persons who live near airport
Copula: are
Predicate:
Complex Numbers
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
10
Algebra
Chapter 10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
Complex Numbers
Introduction
Geometrical Representation of a Complex Number
Polar Form of a Complex Number
Complex con
Continuity
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
3
Calculus I
Chapter 3
Continuity
3.1
2
3.2
Limit of a Function
2
3.3
Properties of Limit of a Function
9
3.4
Two Important Limits
10
3.5
Left and Right Hand Limits
12
3.6
Continuo
1
Rules of implication 1. Modus ponens (MP) 5. Constructive dilemma (CD)
p q p q
2. Modus tollens (MT)
(p q) (r s) p r q s
6. Simplification (Simp)
p q ~q ~p
3. Hypothetical syllogism (HS)
pq p
7. Conjunction (Conj)
p q q r p r
4. Disjunctive syllogism (D
Sets
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
2
Algebra
Chapter 2
Sets
2.1
Introduction
2
2.2
Venn Diagrams
3
2.3
Equality of Sets
3
2.4
Subsets
4
2.5
Empty Set and Singleton
5
2.6
Operations on Sets
5
2.7
Number of Elements in a Fi
Logical, technical, and physical impossibilities, which is which?
Build a computer with 5GHz clock speed. Draw a triangle with internal angles of 200 degrees. To be 300 years of age.
Distinguish between valid and invalid
All cats are animals. All dogs a
Functions
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
1
Calculus I
Chapter 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Functions
Introduction
Direct Images and Inverse Images
Composition of Functions
Constant Function and Identity Function
Injec
Indefinite Integration
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
6
Calculus II
Indefinite Integration
2
Method of substitution
3
Integration by Parts
6
Special Integration
10
Integration of Trigonometric Function
14
Reduction Formula
Inequalities
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
6
Algebra
Chapter 6
Inequalities
Fundamental Concepts of Inequalities and
Methods of Proving Inequalities
2
6.4
Arithmetic Mean and Geometric Mean
7
6.5
Cauchy-Schwarz Inequality
Informal Fallacies
1
Formal Vs Informal Fallacies
A fallacy is a defect in an argument other
than its having false premises.
An informal fallacy is a defect in the
content of an argument. (A formal fallacy is
a defect in the structure of an argument.)
Limit of a Sequence
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
2
Calculus I
Chapter 2
Limit of a Sequence
2.1
2
2.2
Sequences
2
2.3
Convergent Sequences
6
2.4
Divergent Sequences and Oscillating Sequences
7
2.5
Operations on Limits of
Mathematical Induction
Advanced Level Pure Mathematics
AdvancedLevel PureMathematics
3
Algebra
Chapter 3
Mathematical Induction
3.1
First Principle of Mathematical Induction
2
3.2
Second Principle of Mathematical Induction
9
3.1 First Principle of Mathema
Matrices and Determinants
Advanced Level Pure Mathematics
Advanced Level Pure Mathematics
Chapter 8
8
Matrices and Determinants
8.1
INTRODUCTION : MATRIX / MATRICES
2
8.2
SOME SPECIAL MATRIX
3
8.3
ARITHMETRICS OF MATRICES
4
8.4
INVERSE OF A SQUARE MATRIX
Natural Deduction (1)
1
Besides using truth-table to prove the
validity of an argument, we can use another
method, called natural deduction, to do
the same.
Using this method, we can deduce step-bystep the conclusion from the premises with
the help of s