mathhhlogic

51問 • 1年前

問題一覧

Place of fundamental role in mathematics serving as the framework for reasoning proof and the establishment of mathematical truth

logic

Through _____ principles and methods, mathematicians analyze and derive conclusions based on well defined rules and axioms ensuring the consistency and validity of mathematical arguments

logical

Provides the tools to deduce new mathematical theorems established connections between mathematical structures and explore the limits and boundaries of mathematical system

logic

Forms the backbone of the mathematical reasoning enabling mathematicians to explore understand and expand the vast landscape of mathematical concepts and ideas

logic

Extends being on theoretical realms and finds practical application in various real world situations such as problem solving and decision making

logic

It helps in analyzing complex problems and making rational decisions based on logical reasoning

logic

It equips individuals with ability to think critically evaluate arguments and identify fallacies or inconsistencies in reasoning

logic

It plays a crucial role in legal systems where arguments and evidence are evaluated based on logical reasoning

logic

This fundamental for scientific inquiry and scientific method

logic

It is the essential in designing and developing computer systems and software

logic

It is instrumental in the field of artificial intelligence ai and machine learning ml

magic

It is used to formulate hypothesis design statistical tests and draw valid conclusions from data

logic

Sentences or mathematical expressions that can be categorized as either true or false but not both simultaneously

prepositional logic

____ of a proposition represents the factual accuracy or falsehood of the statement

truth value

Serves as a symbolic representation of a proposition or statement

propositional variable

Are commonly employed to the note propositional variables

pq r

Are formed by combining two or more statements using different connectives

compound propositions

Composite propositions are referred to as

compound propositions

A proposition that is not composite is considered

simple proposition

The fundamental property of ___ is that it's truth value is completely determined by the truth values of its subpropositions together with the way in which they are connected to form the compound propositions

compound propositions

The conjunction of the propositions p and q is a compound proposition

p and q p ^ q

The _____ of the propositions p and q is the compound proposition P AND Q BY P ^ Q

conjunction

What are the different logical operation

conjunction disjunction negation

P ^ q is TRUE only when both p and q are ____

true

P or q denoted by P v Q

disjunction

The or in this disjunction is used in the

inclusive sense

The disjunction of the propositions p and q is the compound proposition ____

p or q p v q

The ____ of the proposition p can be formed by writing it does not the case that or it is false that by inserting the word not

negation

Let be the note an expression constructed from propositional variables p q etc which take on the value through the or false f and the logical connectives and or and not such an expression p will be called

proposition

A truth value of the proposition depends exclusively upon the truth values of its variables

yes

A simple concise way to show the relationship of truth value of proposition depending exclusively upon the truth values of its variables

truth table

Conditional prepositions p and q is the compound proposition

if p then q

If p then q P implies q Be only fq

conditional preposition

P ➡️ q The proposition p is called the

hypothesis or antecedent

P ➡️ q The proposition q is called

the conclusion or consequent

Every conditional proposition come in three related phrases that we need to look up to

converse inverse contrapositive

Come in three related phrases that we need to look up to

converse inverse contrapositive

Dubai conditional of the propositions p and q is the compound proposition

p if and only if q p ↔️ q

biconditional proposition

Is a statement or proposition that is always true regardless of the truth values of its individual components

tautology

It is a fundamental concept in propositional logic and plays a significant role in logical reasoning

tautology

Are often used as a basis for logical proofs and reasoning as they provide statements that are universally true

tautology

Can be identified using truth tables where all possible combinations of truth values are analyzed to determine the truth value of the compound proposition

tautology

Tautology is also called as

logically true

Refers to a statement or proposition that is always false regardless of the truth values of its individual components

contradiction

It represents a fundamental inconsistency or logical conflict

contradiction

Contradiction is also called as

logically false or absurd

If the last column of the truth table of the compound proposition gives true and false therefore it is called

contingency

Is an assertion that the given set of prepositions derives another proposition following the laws of logic and rule of inference

argument

Are fundamental in the development of a step by step proof showing how the conclusion logically follows the hypothesis

rules of inference

A need for a technique or list of techniques that somehow bypass the need for constructing any truth tables especially large ones

rules of inference for loss of logic

Business Finance

Sab Sescon · 46問 · 2年前

Business Finance