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The name "disjunctive syllogism" derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that
In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true. [3] It is shown below in logical form. Either A or B Not A Therefore B. When A and B are replaced with real life examples it looks like below.
Disjunctive syllogism ... Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples:
In the 19th century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Immanuel Kant famously claimed, in Logic (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know.
A property in intuitionistic logic stating that if a disjunction is provable, then either is provable or is provable. disjunctive normal form A standardization of logical formulae in which a formula is expressed as a disjunction of conjunctive clauses. disjunctive syllogism
Constructive dilemma is the disjunctive version of modus ponens, whereas, destructive dilemma is the disjunctive version of modus tollens. The constructive dilemma rule can be stated: The constructive dilemma rule can be stated:
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens. The history of modus ponens goes back to antiquity. [4]
A false dilemma can also occur in the form of a disjunctive syllogism: [6] disjunctive syllogism: (), In this form, the first premise is responsible for the fallacious inference. Lewis's trilemma is a famous example of this type of argument involving three disjuncts: "Jesus was either a liar, a lunatic, or Lord". [3]