I would think that it has to start with a conditional exchange, but have no idea where to start. There is a lot of reference to logic on the mises forums, so how about someone on the forums show me that they understand it.

I need help with this one too...

A -> ~A

/ ~A

I thought I was getting good at proofing, but not if there is only one premise.

"The Fed does not make predictions. It makes forecasts..." - Mustang19

Well, you are trying to use Hypothetical Syllogism with two premises. My problem has only one premise and A implies B is not one of them. We do not know that B implies C. We are trying to prove that B doesn't interfere with A's implication of C.

The point of the exercises is to manipulate the inference rules and replacement rules.

"The Fed does not make predictions. It makes forecasts..." - Mustang19

Unfortunately, the precise way of proving logical propositions like these aren't standardized. For your first, you can infer A from "A and B" from a boolean elimination rule called "conjuction elimination".

For your second one, I suppose you can do a proof by contradiction. Suppose A, then since A implies not A, we have A and not A, a contradiction. QED

But without inferring the logical equivalent of the statement of (A^B), which is what that conjunction rule does, idk how you'd even get to the form of the conclusion. You got me man

I don't know what to tell you since the terminology you're using is specific to your class. And your last proof is not logically coherent at all. Look at it carefully.

Here's a proof by cases.

Case 1: A

By the premise, A implies not A. Therefore, not A.

And your last proof is not logically coherent at all. Look at it carefully.

It makes perfect sense. I added links so you can see why it makes sense.

If I am trying to prove ~A, then all I have to do is replace the conditional with a disjunct to present a choice of ~A or ~A. The implication is replaced by a new choice in the dysjunct.