Disjunctive Infer. (XOR)
5-step or more
Disjunctive Inference is a rule of inference pertaining to the OR operator.
Imagine we are given a disjunction: "The patient has an adjustment disorder or he has depression." Let's recognize two distinct statements in this disjunction: 1) The patient has an adjustment disorder, and 2) The patient has depression. Now, if we are told that the patient does not have an adjustment disorder, we have no choice but to conclude that the patient suffers from depression. Formally, it looks like this:
p v q: "The patient has an adjustment disorder or he
The given disjunction p v q and the expression ~p are above the line of dashes, and the conclusion q obtained by applying Disjunctive Inference is below the line.
Other examples of Disjunctive Inference
A v B: "The student passed the quiz or she passed the
X v Y: "The juice is cold or the tea is hot."
Links to Relevant Problems
These are links to validity proof problems whose solutions contain Disjunctive Inference.