英和和英

語源

From contra- +‎ positive.

名詞

contrapositive (plural contrapositives)

1. (logic) The inverse of the converse of a given logical implication.

使用する際の注意点

• From a conditional statement, its inverse, its converse, and its contrapositive are defined as follows:

  Proposition: "If P then Q." ( ${\displaystyle P\rightarrow Q}$)

  Inverse: "If not P then not Q." ( ${\displaystyle \neg P\rightarrow \neg Q}$)

  Converse: "If Q then P." ( ${\displaystyle Q\rightarrow P}$)

  Contrapositive: "If not Q then not P." ( ${\displaystyle \neg Q\rightarrow \neg P}$)

• If a conditional statement is true then its contrapositive is, too. Thus, if the statement "If I'm Roman, then I can speak Latin" is true, then it logically follows that the statement "If I can't speak Latin, then I'm not Roman" must also be true.
  • In classical logic (more generally, logics employing the law of excluded middle), a conditional statement is true if and only if its contrapositive is true. In this framework, if the statement "If I can't speak Latin, then I'm not Roman" is true, then the statement "If I'm Roman, then I can speak Latin" must also be true.
  • This only applies to the contrapositive, while the inverse and the converse do not depend on the original statement.

派生語

参考

• converse
• inverse