

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 
Disjunctive Inference Disjunctive Inference is a rule of inference pertaining to the OR operator. Disjunctive Inference states that in a disjunction, if one of the disjuncts is false, the the other has to be true. This is what is commonly referred to as the process of elimination. 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
has depression." 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
exam." 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. 2step problem (A)
