Destructive dilemma
Rule of inference of propositional logic / From Wikipedia, the free encyclopedia
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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. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false. Destructive dilemma is the disjunctive version of modus tollens. The disjunctive version of modus ponens is the constructive dilemma. The destructive dilemma rule can be stated:
Quick Facts Type, Field ...
Type | Rule of inference |
---|---|
Field | Propositional calculus |
Statement | If implies and implies and either is false or is false, then either or must be false. |
Symbolic statement |
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where the rule is that wherever instances of "", "", and "" appear on lines of a proof, "" can be placed on a subsequent line.