Difference between revisions of "Logic"

Revision as of 11:13, 6 November 2011

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 $q$ "

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. Unknown error_msg) Universal Quantifier: "for all" $\dot$ (Error compiling LaTeX. Unknown error_msg) Existential Quantifier: "there exists"

@@ Line 13: / Line 13: @@
 ==Conjunction==
-The conjunction of two statements basically means "<math>p</math> and <math>q</math>"
+The conjunction of two statements basically means "<math>p</math> and <math>q</math>" and is denoted by <math>p \land q</math>.
 ==Disjunction==

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