Disjunctive inference, also known as disjunctive syllogism or disjunction elimination, is a rule of inference in propositional logic that allows one to draw conclusions from a disjunction and the negation of one of its disjuncts. In other words, if you know that either P or Q is true and you also know that P is not true, then you can infer that Q must be true. Disjunctive inference can be formally represented as follows:
Here’s an example to illustrate disjunctive inference.
Premise: It is either raining or snowing. (R ∨ S)
Premise: It is not raining. (~R)
Conclusion: It is snowing. (S)
Disjunctive inference is a valuable tool in logical reasoning, as it enables one to deduce new information based on the given premises. This rule of inference is commonly used in various fields, including mathematics, computer science, and philosophy, to construct proofs and solve problems.