Difference between revisions of "Logic"
(grammar, notation of inverse and conditional)
m (→Implication, Conditional: wording)
|Line 34:||Line 34:|
statement "If <math>p</math> then <math>q</math>" is denoted by <math>p\implies q</math>. example<math>x+3=5\implies x=2</math> means "If <math>x+3=5</math> then <math>x=2</math>."
Latest revision as of 17:22, 31 July 2020
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 a statement is "A duck is a bird" which is true. Another example is "A pencil does not exist" which is false.
If then . For example, "If it is a duck then it is a bird."
The inverse of the conditional statement is: If not then not .
The converse of the conditional statement is: If then .
The contrapositive of the conditional statement is: If not then not .
The conditional is equivalent to the contrapositive. The inverse is equivalent to the converse. When both the conditional and the converse are true at the same time, this is equivalent to an Iff statement.
- 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 .
The statement "If then " is denoted by . For example, means "If then ."
The converse of the statement is .
The inverse of the statement is .
The contrapositive of the statement is . These statements are logically equivalent.
A truth table 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 .