Difference between revisions of "Logic"

(Implication)
Line 19: Line 19:
  
 
===Implication===
 
===Implication===
This operation is given by the statement "If <math>p</math>, then <math>q</math>". It is denoted by <math>p\Leftrightarrow q</math>. An example is "if  <math>x+3=5</math>, then <math>x=2</math>.
+
This operation is given by the statement "If <math>p</math>, then <math>q</math>". It is denoted by <math>p\implies q</math>. An example is "if  <math>x+3=5</math>, then <math>x=2</math>.
  
 
===Converse===
 
===Converse===

Revision as of 11:47, 21 August 2013

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

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 $\neg p$. $\neg p$ is the statement that is true when $p$ is false and the statement that is false when $p$ is true. This means simply "the opposite of $p$"

Conjunction

The conjunction of two statements basically means "$p$ and $q$" and is denoted by $p \land q$.

Disjunction

The disjunction of two statements basically means "$p$ or $q$" and is denoted by $p \land q$.

Implication

This operation is given by the statement "If $p$, then $q$". It is denoted by $p\implies q$. An example is "if $x+3=5$, then $x=2$.

Converse

The converse of the statement $p \Leftrightarrow q$ is $q \Leftrightarrow p$.

Contrapositive

The contrapositive of the statement $p \Leftrightarrow q$ is $\neg p \Leftrightarrow \neg q$

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 $\forall$ and an existential quantifier is denoted by $\exists$.

See Also

Invalid username
Login to AoPS