Disjunctive Infer. (XOR)
5-step or more
Mutual Exclusion is a rule of inference pertaining to the XOR operator.
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 married Paul, we have no choice but to conclude that she did not marry Alex. Formally, it looks like this:
p XOR q: "Alice married Alex or Paul."
The given exclusive disjunction p XOR q and the expression q are above the line of dashes, and the conclusion ~p obtained by applying the Mutual Exclusion rule is below the line.
Other examples of Mutual Exclusion
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 Mutual Exclusion.