Difference between revisions of "Logic"
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==Quantifiers== | ==Quantifiers== | ||
| − | There are two types of quantifiers: | + | There are two types of quantifiers: A universal Quantifier: "for all" and an existential Quantifier: "there exists". A universal quantifier is denoted by <math>\forall</math> and an existential quantifier is denoted by <math>\exists</math>. |
| − | <math>\ | ||
| − | <math>\ | ||
==See Also== | ==See Also== | ||
Revision as of 11:19, 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 
" and is denoted by 
.
Disjunction
The disjunction of two statements basically means " or " and is denoted by .
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
A truth tale is the list of all possible values of a compound statement.
Quantifiers
There are two types of quantifiers: A universal Quantifier: "for all" and an existential Quantifier: "there exists". A universal quantifier is denoted by 
and an existential quantifier is denoted by 
.
