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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.
15 lip 2018 · The contrapositive of a statement negates the conclusion as well as the hypothesis. It is logically equivalent to the original statement asserted. Often it is easier to prove the contrapositive than the original statement.
It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
2 wrz 2024 · Noun. [edit] contrapositive (plural contrapositives) (logic) The inverse of the converse of a given logical implication. Usage notes. [edit] From a conditional statement, its inverse, its converse, and its contrapositive are defined as follows: Proposition: "If P then Q." Inverse: "If not P then not Q." Converse: "If Q then P."
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction.
28 sie 2024 · Proof by Contraposition is a rule of inference used in proofs. This rule infers a conditional statement from its contrapositive. It is based on the Rule of Transposition, which says that a conditional statement and its contrapositive have the same truth value: $p \implies q \dashv \vdash \neg q \implies \neg p$. In other words, the conclusion:
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.
