How do you do a proof in propositional logic of an argument containing no premises, only a conclusion?

Answer 1

It depends on what you're trying to prove. But my first attempt would be to negate the conclusion and attempt a proof by contradiction.

In other words, if your conclusion is "A," then your proof would look something like:
1. Assume "not A" is true.
2. If "not A" is true, than "B" and/or "C" are true.
3. If "B" is true, then...
4. Etc.
.
.
n. But that results in a contradiction.
n+1. Therefore "not A" is false, meaning "A" is true.

This isn't guaranteed to work, of course, but it's worth a shot.

Answer 2

You have to work backwards in logic.
Take the conclusion and figure out what could be the premise for that particular conclusion.