# Difference between revisions of "Logic"

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===Contrapositive=== | ===Contrapositive=== | ||

− | The contrapositive of the statement <math>p \ | + | The contrapositive of the statement <math>p \implies q</math> is <math>\neg p \implies \neg q</math>. These statements are logically equivalent. |

==Truth Tables== | ==Truth Tables== |

## Revision as of 11:52, 21 August 2013

**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

The negation of , denoted by , is the statement that is true when is false and is false when is true. This means simply "it is not the case that ."

### Conjunction

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

### Disjunction

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

### Implication

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

### Converse

The converse of the statement is .

### Contrapositive

The contrapositive of the statement is . These statements are logically equivalent.

## Truth Tables

A truth tale is the list of all possible values of a compound statement.

## Quantifiers

There are two types of quantifiers: A universal Quantifier: "for all" and an existential Quantifier: "there exists". A universal quantifier is denoted by and an existential quantifier is denoted by .