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Then the converse of S is the statement Q implies P (Q → P). In general, the truth of S says nothing about the truth of its converse, [2] unless the antecedent P and the consequent Q are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal."
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 ...
" In this case, unlike the last example, the inverse of the statement is true. The converse is "If a polygon has four sides, then it is a quadrilateral." Again, in this case, unlike the last example, the converse of the statement is true. The negation is "There is at least one quadrilateral that does not have four sides.
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 ...
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.
A logical fallacy in which a conditional statement is incorrectly used to infer its converse. For example, from "If P then Q" and "Q", concluding "P". alethic modal logic A type of modal logic that deals with modalities of truth, such as necessity and possibility. ambiguity
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected ...
In logic, converse nonimplication [1] is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication). Definition [ edit ]