Could be nice to add a concrete "real-life" (non-math) example, say like the following:

You are a defense lawyer. Your client is accused of *stealing the cookie from the cookie jar*. You want to prove her innocence. Lets say you have evidence that the jar is still sealed. Reason as follows:

- Assume she stole the cookie from the cookie jar.
- Then she would have had to open the jar.
- The jar is still sealed.
- For the jar to be sealed and for her to have opened it is a contradiction.
- Hence the assumption in 1 is false (given the deductions below it are true).
- Hence she did
*not*steal the cookie from the cookie jar.

(Yes, I'm sure you can still figure out a way in which she stole the cookie. You're very clever. This is just an example to illustrate the method.)