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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 ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...
converse domain In set theory and logic, the set of all elements that are related to any element of a given set under a specific relation. [72] converse barcan formula A principle in modal logic suggesting that possibility precedes existence, the converse of the Barcan formula. conversion
The name converse arises because the reversal of arrows corresponds to taking the converse of an implication in logic. The name transpose is because the adjacency matrix of the transpose directed graph is the transpose of the adjacency matrix of the original directed graph.
A naïve understanding of the converse says that the converse of this is: (B → C) → A But in fact, as mathematicains and logicians understand and use the word "converse", the original proposition is understood to be equivalent to : (A ∧ B) → C and so its converse is: C → (A ∧ B).
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
The converse relation does satisfy the (weaker) axioms of a semigroup with involution: () = and () =. [12] Since one may generally consider relations between different sets (which form a category rather than a monoid, namely the category of relations Rel ), in this context the converse relation conforms to the axioms of a dagger category (aka ...