Difference between revisions of "Logic"
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This operation is given by the statement "If <math>p</math>, then <math>q</math>". It is denoted by <math>p\
This operation is given by the statement "If <math>p</math>, then <math>q</math>". It is denoted by <math>p\q</math>. An example is "if <math>x+3=5</math>, then <math>x=2</math>.
Revision as of 11:47, 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.
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 "
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
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 .