MMW - Chapter 2

Mathematics as a Language

R

Real Numbers

Q

Rational Numbers

Q’

Irrational Numbers

Z

Integers

N

Natural Numbers

Open Sentence

Uses variables

Closed Sentence

known to be either true or false

Set

well-defined collection

Rule Method

uses a phrase that describes the property of the elements

Roster Method

lists the elements

Subset ⊆

if tanan element A naa sa element B

Intersection ∩

unsa ang common nga element

Union ∪

sapar (bawal balik)

Universal Set U

Tanan

Complement of a SET’

element nga wala sa set

Cartesian Product

bali bali, x belong to y, y belong to x

Relation

a relationship between sets of values

Function

an assignment of one element of Y to each element of X

Logic

the study of methods of reasoning or argumentation

Proposition

declarative sentence that is either true or false, but nnot bo

Simple proposition

contains only one idea

Compound proposition

at least two simple proposition joined by logical connectives

Negation ~

not

Conjunction ∧

and

Disjunction ∨

or

Conditional →

if, then

Biconditional ⇔

if and only if

Contradiction

‘false’ for all possible truth values

Tautology

‘true’ for all possible truth values

Contingency

neither tautology nor a contradiction

Satisfiability

at least ONE true in truth values

∃

there exist

∀

For all

Inductive Reasoning

Specific observation, General conclusion (bottom-up) THEORY

Deductive Reasoning

General statement, Specific conclusion (top-down) FORMULA

Valid argument

if the conclusion is true

Invalid argument

if the conclusion is false