Revision as of 12:13, 6 November 2011 by Thkim1011 (talk | contribs) (Conjunction)

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


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.


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 $p$"


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


The disjunction of two statements basically means "$p$ or $q$"


This operation is given by the statement "If $p$, then $q$". It is denoted by $p\Leftrightarrow q$


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


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

Truth Tables


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"

See Also

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