Logic: Difference between revisions
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==Implication== | ==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> | This operation is given by the statement "If <math>p</math>, then <math>q</math>". It is denoted by <math>p\Leftrightarrow q</math>. An example is "if <math>x+3=5</math>, then <math>x=2</math>. | ||
==Converse== | ==Converse== | ||
Revision as of 11:21, 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 
. 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 
. An example is "if 
, then 
.
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 
.
