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In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive.
contrapositive: If \(f\) is not differentiable, then it is not continuous. converse: If \(f\) is differentiable, then it is continuous. inverse: If \(f\) is not continuous, then it is not differentiable.
28 lis 2020 · contrapositive: If a conditional statement is \(p\rightarrow q\) (if \(p\) then q), then the contrapositive is \(\sim q\rightarrow \sim p\) (if not q then not p). converse: If a conditional statement is \(p\rightarrow q\) (if \(p\), then \(q\)), then the converse is \(q\rightarrow p\) (if \(q\), then \(p\).
The contrapositive: if not Q then not P. The inverse: if not P then not Q. The converse: if Q then P. It turns out that the \original" and the \contrapositive" always have the same truth value as each other. Also, the \inverse" and the \converse" always have the same truth value as each other.
11 lis 2022 · The contrapositive of an implication is the converse of its inverse (or the inverse of its converse, which amounts to the same thing). That is, \[\text{ the contrapositive of } A\Rightarrow B\text{ is the implication }\lnot B\Rightarrow\lnot A\]
3 sie 2024 · The converse of the conditional statement is “If Q then P.”. The contrapositive of the conditional statement is “If not Q then not P.”. The inverse of the conditional statement is “If not P then not Q.”. We will see how these statements work with an example.
An implication is a statement of the form “If P is true, then Q is true.”. P is called the antecedent and Q is called the consequent. The contrapositive of the implication “If P is true, then Q is true” is the implication “If Q is false, then P is false.”.
