TOPIC 3 : LEGAL ASPECTS OF
BUSINESS ENTITIES
LEARNING OBJECTIVES :
Discuss types of business entities in Malaysia in
respect of formation, management, liability and
dissolution.
Describe sole proprietorship
Describe partnership
Discuss Registered Compan
At the end of the period, you should be able to:
Identify propositions from non-propositions.
(CO1, CO2)
Perform operations on simple or compound
propositions using logical operators.
(CO1, CO2)
Find truth values of simple or compound
propositions, con
At the end of the period, you should be
able to:
Show logical equivalences of conditional
or biconditionals statements. (CO1,
CO2)
Note: If p and q are logically equivalent,
the symbol p q (p is equivalent to q) is
also used.
Two propositions are said
LOGO
Introduction to Proofs
LOGICAL PROOFS
A mathematical system consists of
Undefined terms
Definitions
Axioms
Theorems etc.
LOGICAL PROOFS
Undefined terms are the basic building blocks
of a mathematical system.
These are words that are accepted as s
LOGO
Predicates and Quantifiers
Predicates
The sentence x + 2 = 2x is not a proposition,
but if we assign a value for x then it becomes a
proposition.
The phrase x + 2 = 2x can be treated as a
function for which the input is a value of x and the
output i
LOGO
Logical Equivalences and
the Rules of Replacement
RULES OF REPLACEMENT
1. Idempotent Laws
pp p
pp p
2. Transposition
(pq) (q p)
3. Double Negation Law
(p) p
4. De Morgans Laws
(pq) (p q)
(pq) (p q)
RULES OF REPLACEMENT
5. Commutative Laws
pq q
Mathematical Induction
A standard procedure for establishing
the validity of mathematical statements
which we shall call as propositions
involving a series of positive integers.
Mathematical Induction
First Principle of Mathematical Induction
Let P(n) be
PROBLEM SOLVING
1. Gregor Mendel used the traits of pea plants to formulate his laws of inheritance. Suppose that the
allele for axial (A) flower position in peas is dominant over the terminal (a) flower position, apply
Mendels principles to predict the p
4. Organize the activities beforehand. As a road map on unfamiliar territory,
it allows the entrepreneur to estimate how the business Will perform in the
future and to prepare for Contingencies 1n case things will not turn out as
planned. .
Assess actual
Ellipse
An ellipse is formed when a plane cuts only one of the cones, but is
neither parallel to the axis nor parallel to the a generator.
ELLIPSE
Definition
An ellipse is the set of all points P in a plane
such that the sum of the distances of P from
t
BIO06: General Biology 2
Laboratory Exercise No. 4
The Monohybrid Cross and Pedigree Analysis
INTRODUCTION
In 1865, long before our modern understanding of genetics and DNA, a scientist named Gregor Mendel
discovered some of the secrets of inheritance and
BIO06: General Biology 2
Laboratory Exercise No. 8
Genetic Drift: Founder Effect vs. Bottleneck Effect
INTRODUCTION
Genetic drift is defined as the random change in allele frequencies that occurs in small populations. It is
not due to natural selection. G
BIO06: General Biology 2
Laboratory Exercise No. 2
Squid Dissection
(Invertebrate Anatomy and Physiology)
INTRODUCTION
Squid is one of the most highly developed invertebrates. It is included in the phylum Mollusca derived from the
Latin word mollis mea
BIO06: General Biology 2
Laboratory Exercise No. 5
Gene Interaction, Epistasis, and The Dihybrid Cross
INTRODUCTION
Gene interaction is the collaboration of several different genes in the production of one phenotypic character
(or related group of charact
BIO06: General Biology 2
Laboratory Exercise No. 7
The Chips are Down: A Simulation of Natural Selection
INTRODUCTION
The process of natural selection occurs because organisms vary in their heritable characteristics, and because
some variants survive and
BIO06: General Biology 2
Laboratory Exercise No. 1
Water Running Uphill
INTRODUCTION
Humans spend a tremendous amount of energy transporting water from underground springs, streams, and
lakes to wherever it is needed. The methods they use vary from a buck
FUNCTION
As a Rule
As a Set of Ordered Pairs
Concept of function
We may imagine a function to be some sort of a box or
machine. When something is fed into the machine, there
will be an output. The output must be unique. This means
that no matter how many
LOGIC
1
Truth table
A proposition may consist of other propositions. The truth
value of this proposition may change depending on the truth
values of the other propositions it is made of. The truth
values for all possible cases are displayed in tabular for
Equivalence
Relation
Reflexive, Symmetric, and Transitive
Definition. A binary relation on a set is called an
equivalence relation if it is reflexive, symmetric, and
transitive.
Example. Let and
The table below gives the properties of the five relations.
LOGIC
Predicates and Quantifiers
Let be a non-negative integer. An -place predicate is a
statement containing variables. By fixing the values of the
variables in a predicate, it becomes a proposition.
0-place predicate
1-place predicate
2-place predicate
BINARY RELATION
Definition. A binary relation on a set is any subset of .
Example. Let . Then
, (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)
By definition, a binary relation on is any subset of .
Therefore, the following are binary relations on the set :
Note
Principle of Inclusion
and Exclusion
Principle of Inclusion and Exclusion
Let , , , be arbitrary sets. Then
Examples
Exercise. Write the formula for using the principle of
inclusion and exclusion.
Illustration for
The red circle means that the elements in
ORDERING
RELATIONS
PARTIAL ORDERING
LINEAR ORDERING
Let us first discuss a new and more convenient notation for
membership in a binary relation. If is a binary relation on a
set , then the statement will be written as .
Example. Consider the binary relati
Special Binary
Relations
Special relations
Definition. A binary relation on a set is reflexive if for
all , .
Example. Let . Consider the following binary relations
on :
1.
2.
3.
Among the three given relation, only and are reflexive.
Note that for any se
CGC Visit
Write down your reflections here:
During the CGC visit, the facilitator discussed to us the results from the previous personality test we had during the 6 th week. The trend in
Week 10
Name: Chavez, Katrina Jell S.
Section: C46
RUBRICS FOR GRADI
Course Synthesis
Week 11
Name: Chavez, Katrina Jell S.
Section: C46
HOW VE012 CHANGED MY PERSPECTIVES:
Values 2 changed my perspective towards my ultimate goal in life. Now, I want to be someone who is not just excellent in the
field that Im up to but als
Levels of Leadership
The first negative aspect that I need to conquer in order to be good in my personal leadership is procrastination. I put off things that I should
be focusing on right now, usually in favor of doing something that is more enjoyable or
Levels of Leadership
A Common Mistake
Most leadership seminars and courses
focus on improving ones leadership skills
in the context of leading a team, an office,
or an organization.
A Common Mistake
Thats good. But let us realize
that leadership is not on
Chavez, Katrina Jell
Written Report
Llana, Mervin Floyd
Leaders Profile
Nerveza, Jashmin Kimson M.
Mrs. Marife Castillo
Ratena, Czarina
March 15, 2016
Dean Joy Hofilea is a graduate of B.S. in Chemistry at Siliman University in Dumaguete City. She
got her
CGC Visit
Exer.4
Name: CHAVEZ,
KATRINA JELL
Section: A06
Write down your reflections here:
Last meeting, Maam April from CGC discuss to us the importance of self discipline. Self-discipline is one of the most important and useful skills
everyone should po