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In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...
Converse nonimplication is notated , which is the left arrow from converse implication (), negated with a stroke (/). Alternatives include p ⊄ q {\textstyle p\not \subset q} , which combines converse implication's ⊂ {\displaystyle \subset } , negated with a stroke ( / ).
Converse (logic), the result of reversing the two parts of a definite or implicational statement Converse implication, the converse of a material implication; Converse nonimplication, a logical connective which is the negation of the converse implication; Converse (semantics), pairs of words that refer to a relationship from opposite points of view
Conversion (the converse), "If I wear my coat, then it is raining ." The converse is actually the contrapositive of the inverse, and so always has the same truth value as the inverse (which as stated earlier does not always share the same truth value as that of the original proposition).
The converse of the last implication does not hold in pure intuitionistic logic. That is, the failure of the joint proposition cannot necessarily be resolved to the failure of either of the two conjuncts. For example, from knowing it not to be the case that both Alice and Bob showed up to their date, it does not follow who did not show up.
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
Logical consequence (also entailment or implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
The converse does however not hold in general, unless the excluded middle statement at hand is stable itself. An implication ψ → ¬ ϕ {\displaystyle \psi \to \neg \phi } can be proven to be equivalent to ¬ ¬ ψ → ¬ ϕ {\displaystyle \neg \neg \psi \to \neg \phi } , whatever the propositions.