Disjunctive Infer. (XOR)
5-step or more
Disjunctive Inference with XOR
Disjunctive Inference with XOR is a rule of inference pertaining to the XOR operator.
Disjunctive Inference with XOR states that in an exclusive disjunction, if one of the exclusive disjuncts is false, then the other has to be true. This is what is commonly referred to as the process of elimination.
Imagine we are given an exclusive disjunction: "Alice married Alex or Paul." We know that this is an exclusive disjunction as opposed to a regular disjunction because Alice could not have married both Alex and Paul. Let's recognize two distinct statements in this exclusive disjunction: 1) Alice married Alex, and 2) Alice married Paul. Now, if we are told that Alice did not marry Alex, we have no choice but to conclude that she married Paul. Formally, it looks like this:
p XOR q: "Alice married Alex or Paul."
The given exclusive disjunction p XOR q and the expression ~p are above the line of dashes, and the conclusion q obtained by applying Disjunctive Inference with XOR is below the line.
Other examples of Disjunctive Inference with XOR
A XOR B: "The client is in Austria or Germany."
X XOR Y: "The cafeteria food is acceptable or appalling."
Links to Relevant Problems
These are links to validity proof problems whose solutions contain Disjunctive Inference with XOR.