contraposition

contraposition

A clear example of contraposition can be seen in the concepts of day and night.

Definition
  1. Noun:
    • Logical opposition: In logic, "contraposition" refers to the act of forming the contrapositive of a statement, which involves swapping and negating the subject and predicate of a conditional proposition (e.g., "If P, then Q" becomes "If not Q, then not P").
    • Contrast or opposition: A general sense of being placed in opposition or contrast to something else.
Usage Examples

  • Logical opposition:

    • The validity of the argument was tested through contraposition. (The logical process of converting the conditional statement was applied.)
    • In mathematics, contraposition is used to prove theorems by showing that if the conclusion is false, then the premise must also be false.

  • Contrast or opposition:

    • The two ideas are in contraposition, highlighting their fundamental differences. (They are placed in direct opposition to each other.)
Advanced Usage

  • "the contrapositive": A specific term in logic for the statement formed by contraposition.

    • The contrapositive of "If it rains, the ground is wet" is "If the ground is not wet, it does not rain." (This logical equivalent is always true if the original statement is true.)

  • "in contraposition to": meaning in direct opposition or contrast to.

    • Her opinion stood in contraposition to the majority view. (Her opinion was directly opposed to the majority.)
Variants and Related Words

  • Contrapositive (adj/n): relating to or being the statement formed by contraposition.

    • The contrapositive statement is logically equivalent to the original. (The swapped and negated version is valid.)

  • Contrapose (verb): to place in opposition or contrast.

    • The author contrapose the two characters to highlight their differences. (The author sets them in opposition.)
Synonyms
  • Opposition: the state of being against or in conflict.
  • Contrast: the state of being strikingly different.
  • Antithesis: a person or thing that is the direct opposite of someone or something else.
Related Idioms
  • "In opposition to": directly against or contrary to.
    • His actions were in opposition to his stated beliefs. (His actions contradicted his beliefs.)