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Destructive dilemma [1] [2] is the name of a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either Q is false or S is false, then either P or R must be false.
There is a slightly different version of dilemma that uses negation rather than affirming something known as destructive dilemma. When put in argumentative form it looks like below. When put in argumentative form it looks like below.
Constructive / destructive dilemma; ... Modus ponendo tollens (MPT; [1] Latin: "mode that denies by affirming") [2] is a valid rule of inference for propositional logic.
Constructive dilemma [1] [2] [3] is a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either P or R is true, then either Q or S has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too.
The term dilemma is attributed by Gabriel Nuchelmans to Lorenzo Valla in the 15th century, in later versions of his logic text traditionally called Dialectica. Valla claimed that it was the appropriate Latin equivalent of the Greek dilemmaton. Nuchelmans argued that his probable source was a logic text of c. 1433 of George of Trebizond. [2]
In logic, there are two main types of inferences known as dilemmas: the constructive dilemma and the destructive dilemma. In their most simple form, they can be expressed in the following way: [7] [6] [1] simple constructive: (), (), ()
destructive dilemma A form of argument involving two conditional statements and their negated consequents, leading to the negation of at least one of the antecedents. determiner A word, phrase, or affix that specifies the reference of a noun or noun phrase, such as "the", "some", "every". deterministic polynomial time
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.