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.)