Disjunctive Infer. (XOR)
5-step or more
Simplification is a rule of inference pertaining to the AND operator.
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.