Difference between revisions of "Logic"
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'''Logic''' is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument. | '''Logic''' is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument. | ||
| − | ==Logical | + | ==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}} | {{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== | ||
| − | + | ==Quantifiers== | |
| + | There are two types of quantifiers: | ||
| + | <math>\dot</math> Universal Quantifier: "for all" | ||
| + | <math>\dot</math> Existential Quantifier: "there exists" | ||
==See Also== | ==See Also== | ||
*[[Dual]] | *[[Dual]] | ||
| − | |||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Logic]] | [[Category:Logic]] | ||
Revision as of 00:59, 6 November 2011
Logic is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument.
Contents
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 
. is the statement that is true when 
is false and the statement that is false when is true. This means simply "the opposite of "
Conjunction
The conjunction of two statements basically means " and 
"
Disjunction
The disjunction of two statements basically means " or "
Implication
This operation is given by the statement "If , then ". It is denoted by 
Converse
The converse of the statement 
is 
.
Contrapositive
The contrapositive of the statement is 
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"
