STUDY OF PATTERNS

mathematics

study of patterns. studying pattern is an opportunity to observe, hypothesis, experiment, discover and create

study of patterns

an arrangement which helps observers anticipate what they might see or what happened next

logic patterns

usually the first to be observed. classifying things, for example, comes before the numeration

number patterns

it helps to predict the events.

such as 2,4,6,8,10

geometric patterns

a motif or design that depicts abstract shapes like lines, polygons, and circles, typically repeats like a wallpaper

word patterns

found in language like the morphological rules on pluralizing nouns or conjugating verb for tense, as well as the metrical rules of the proetry

mathematical language

language is a systematic means of communicating by the use of sounds or conventional symbols

logic

the study of the techniques and principles used to differentiate accurate reasoning from inaccurate reasoning

logic

it aims to find and create a standard use to evaluate arguments and to classify good arguments from bad ones

proposition

statement or assertion that expresses a judgement or opinion

proposition

building block of an argument. something that may be asserted or denied

proposition

it can assert that something is true or false

sentence

it is an idea expressed in words like question, command, an exclamation. the express no judgement of what is right or wrong

simple proposition

declarative sentence subject for affirmation or denial, and with truth value; either true (T) or false (F), but not both

subject term

designates the idea about which the assertion is made

predicate term

it designates the idea which is asserted is denied of the subject

copula

such as "are" and "are not"

copula

expresses the present act of the idea, hence the verb "to be" is used in the present tense even though the assertion is passed or yet to be made.

copula

it makes the proposition affirmative or negative

qualifiers

such as "all", "no", and "some"

qualifiers

specifies the quantity or propositions

universal prep

subject is taken in full extent

(ALL)

particular prep

subject is only taken in particular extent (SOME)

singular prep

subject denotes a SINGLE person/thing

affirmative (universal)

all...is...

negative (universal)

all...is not...

affirmative (particular)

some...is...

negative (particular)

some...is not...

syllogism

the cornerstone of mathematical logic, deals with hypothetical or compound proposition

compound proposition

a proposition formed by combining two or more simple categorical propositions, we're connectives are used

truth value

what are the resulting proposition (combine propositions using connectives) is TRUE or FALSE

truth table

tubular diagram of truth values

conjunction

a proposition which is the result of combining two other propositions (conjunctions) with the connective and

conjunction (p^q)

if both statement is true both are true

disjunction (pvq)

a proposition which is the result of combining two other propositions with the connective or

disjunction (p v q)

if the both statement if false both are false

implication/ conditional (p arrow to the right q)

a proposition which is the result of combining a hypothesis (antecedent) to a conclusion (consequent) in the form if...,then...

implication/conditional (p arrow to right q)

equivalence/bioconditional

a proposition which is the result of combining two propositions in the form ...if and only if... (iff)

equivalence/bioconditional (p arrow both left & right)

the equivalence is true if both are true

the equivalence is false if both are false

negation (~p)

proposition which is the result of reversing the truth value of a given proposition (opposite)