What Is a "Contrapositive Statement"?

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    Form

    • If a statement is expressed as "P => Q," or "If P, then Q," a contrapositive statement then takes the form "~Q => ~P," or "If not Q, then not P."

    Examples

    • An example of a statement is "If John is sweating, then it is warm outside." The contrapositive of this statement would be "If it is not warm outside, then John is not sweating." A contrapositive does not have to be a true statement. It only needs to share a truth value with the original statement.

    Uses

    • Contrapositive statements are often used in logical mathematical proofs, as they are sometimes easier to prove than the original statement.

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