

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 
Simplification Simplification is a rule of inference pertaining to the AND operator. Simplification means that in a given conjunction, any conjunct can be separated out and is true. Imagine we are given the following conjunction: "Negotiations failed and war was declared." Let's recognize two distinct conjuncts in that sentence: 1) Negotiations failed, and 2) War was declared. If we are told that the entire conjunction is true, we have to conclude that each of the conjuncts must also be true. In other words, the statement "negotiations failed" is true, and the statement "war was declared" is true as well. Formally, we would write: p ^ q: "Negotiations failed and war was declared." The given conjunction p ^ q is above the line of dashes, and the conclusions p and q obtained by applying the Simplification rule are below the line.
Other examples of Simplification A ^ B: "The book was interesting and the movie was boring."
~Y ^ X: "It's not windy and it's humid."
Links to Relevant Problems These are links to validity proof problems whose solutions contain Simplification. 2step problem
