Logic: Difference between revisions

Revision as of 23:59, 5 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 $q$ "

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 1: / Line 1: @@
 '''Logic''' is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument.
-==Logical Notation==
+==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|Logical notation}}
-'''Logical notation''' is a special syntax that is shorthand for logical statements.
+A '''Logical notation''' is a special syntax that is shorthand for logical statements.
+==Negations==
+A negation is denoted by <math>\neg p</math>. <math>\neg p</math> is the statement that is true when <math>p</math> is false and the statement that is false when <math>p</math> is true. This means simply "the opposite of <math>p</math>"
+==Conjunction==
+The conjunction of two statements basically means "<math>p</math> and <math>q</math>"
+==Disjunction==
+The disjunction of two statements basically means "<math>p</math> or <math>q</math>"
+==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>
+==Converse==
+The converse of the statement <math>p \Leftrightarrow q</math> is <math>q \Leftrightarrow p</math>.
+==Contrapositive==
+The contrapositive of the statement <math>p \Leftrightarrow q</math> is <math>\neg p \Leftrightarrow \neg q</math>
+==Truth Tables==
-For example, both <math>p\to q</math> and <math>p \subset q</math> mean that <math>p</math> ''implies'' <math>q</math>, or "If <math>p</math>, then <math>q</math>."
+==Quantifiers==
+There are two types of quantifiers:
+<math>\dot</math> Universal Quantifier: "for all"
+<math>\dot</math> Existential Quantifier: "there exists"
 ==See Also==
 *[[Dual]]
-{{stub}}
 [[Category:Definition]]
 [[Category:Logic]]

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