# Logic

**Logic** is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument.

## Contents

## Statements

A statement is either true or false, but it will never be both or neither. An example of statement can be "A duck is a bird." which is true. Another example is "A pencil does not exist" which is false.

## Logical Notations

*Main article: Logical notation*

A **Logical notation** is a special syntax that is shorthand for logical statements.

## Negations

A negation is denoted by . is the statement that is true when is false and the statement that is false when is true. This means simply "the opposite of "

## Conjunction

The conjunction of two statements basically means " and " and is denoted by .

## Disjunction

The disjunction of two statements basically means " or "

## Implication

This operation is given by the statement "If , then ". It is denoted by

## Converse

The converse of the statement is .

## Contrapositive

The contrapositive of the statement is

## Truth Tables

## Quantifiers

There are two types of quantifiers: $\dot$ (Error compiling LaTeX. ! Extra }, or forgotten $.) Universal Quantifier: "for all" $\dot$ (Error compiling LaTeX. ! Extra }, or forgotten $.) Existential Quantifier: "there exists"