Case analysis: try every case
When you don’t know which case you are in, check them all. If every case ends the same way, that is your conclusion.
How it works
Case analysis starts with a list of possibilities that covers everything. Then you work through each one.
It is used two ways. If every case leads to the same conclusion, the conclusion holds, even though you never learned which case is real. If every case but one leads to a contradiction, the survivor is the answer.
Knights and Knaves is built for the second way. Two islanders give four cases. Cross out the ones where a knight lies or a knave tells the truth.
Worth memorizing
List cases that cover every possibility.
Cube or not a cube. Knight or knave. Each value a cell could take.
If every case gives the same result, you have it.
You never needed to know which case is real.
If all cases but one break, the survivor is the answer.
This is elimination with a contradiction doing the ruling out.
Practice
0 of 5 right- A says: “If I am a knight, then so is B.”
- A says: “B and I are the same kind.”
- B says: “A is a knave.”
Every piece is small or large. If it is small, it adjoins a. If it is large, it adjoins a. What follows?