Truth trees work by creating a contradiction. We take a statement that we want to prove true, turn it around by negating it, and then show that that negation leads to contradictions.
For example, I can use this basic method to prove that there isn’t a largest even number, N:
Example: Prove there is no such thing as a largest even number, N.
We’ll start by inverting the fact to prove, and then we’ll show that it leads to a contradiction. Suppose that there is a largest even number, N.
Since N is the largest even number, then for every other even number n, n < N.
N is a natural number; therefore, it can be added with other natural numbers.
If we add 2 to N, the result will be even and it will be larger ...