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3 Αυγ 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.
In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form P → Q {\displaystyle P\rightarrow Q} , the inverse refers to the sentence ¬ P → ¬ Q {\displaystyle \neg P\rightarrow \neg Q} .
28 Νοε 2020 · inverse: If a conditional statement is \(p\rightarrow q\), then the inverse is \(\sim p\rightarrow \sim q\). Logically Equivalent: A statement is logically equivalent if the "if-then" statement and the contrapositive statement are both true. premise: A premise is a starting statement that you use to make logical conclusions.
The inverse of the conditional \(p \rightarrow q\) is \(\neg p \rightarrow \neg q\text{.}\) The contrapositive of this new conditional is \(\neg \neg q \rightarrow \neg \neg p\text{,}\) which is equivalent to \(q \rightarrow p\) by double negation.
11 Ιαν 2023 · Four testable types of logical statements are converse, inverse, contrapositive and counterexample statements. Learn step-by-step with these examples and video.
21 Νοε 2023 · What is an example of an inverse statement? Consider the statement "if the stoplight is green, then go." The inverse of this statement is, "if the stoplight is not green, then don't go." Is the...
As an example of an invertible rule, consider ^R again: A ! ^R. A ^ B. The premises already imply the conclusion since the rule is sound. So for ^R to be invertible means that if the conclusion holds then both premises hold as well. That is, we have to show: If ! A ^ B then ! A and ! B, which is the opposite of what the rule itself expresses.
