

Sample sentences AND operator IF/THEN operator NOT operator OR operator XOR operator Chain Rule Conjunctive Addition Contrapositive DeMorgan's Law Disjunctive Addition Disjunctive Inference Disjunctive Infer. (XOR) Double Negation Modus Ponens Modus Tollens Mutual Exclusion Simplification 2step 3step 4step 5step or more Bad Argument 
Mutual Exclusion Mutual Exclusion is a rule of inference pertaining to the XOR operator. Mutual Exclusion states that in an exclusive disjunction, if one of the exclusive disjuncts is true, then the other has to be false. 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.
