Logic

Revision as of 23:59, 5 November 2011 by Thkim1011 (talk | contribs)

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 $q$"

Disjunction

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

Implication

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

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

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"

See Also

Invalid username
Login to AoPS