How would I convert this sentence to propositional logic?

Question

Kant is a transcendental idealist, unless Hume isn’t an empiricists.

Either Leibniz is not a rationalist or Hume is an empiricists.

Leibniz is a rationalist.

So, Kant is a transcendental idealist.

I think it would be something like:

p -> ~q

~r v q

r

therefore

p

would this be right?

Answer 1

TIP

"P unless Q" can be paraphrased as "P if not Q"

Here is an example "You won't pass the course unless you complete all the assignments".

This clearly means that "if you don't complete all the assignments, you won't pass the course."

Also: it does not mean that if you do complete all the assignments, you will pass the course ... you better get some passing scores on the quizzes as well, for example.

So yes: translate "P unless Q" as $\neg Q \rightarrow P$

Answer 2

The first one should be $q\to p$. We have that either Kant is a transcendental idealist, or Kant not is a transcendental idealist and Hume isn’t an empiricist. (No "s" at the end. One empiricist, many empiricists.) That is $$p\vee(\neg p \wedge \neg q)\iff p\vee\neg q\iff q\to p$$