Difference between revisions of "Logic"
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The contrapositive of the statement <math>p \implies q</math> is <math>\neg
The contrapositive of the statement <math>p \implies q</math> is <math>\neg \implies \neg </math>. These statements are logically equivalent.
Revision as of 11:54, 21 August 2013
Logic is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument.
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.
- Main article: Logical notation
A Logical notation is a special syntax that is shorthand for logical statements.
The negation of , denoted by , is the statement that is true when is false and is false when is true. This means simply "it is not the case that ."
The conjunction of two statements basically means " and " and is denoted by .
The disjunction of two statements basically means " or " and is denoted by .
This operation is given by the statement "If , then ". It is denoted by . An example is "if , then .
The converse of the statement is .
The contrapositive of the statement is . These statements are logically equivalent.
A truth tale is the list of all possible values of a compound statement.
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 .