Come on people, I am mostly wondering how [ [Q^R] therefore S] would break down...

Here is what I have gathered


Facts: P = True , P->Q = True, R= True, Q^R -> S =True

So taking P and P -> Q, we derive Q by Modus Ponens
Then We take R and Q and get Q^R by conjunction
Then we take Q^R and Q^R -> S to get S by Modus Ponens.

Is this what you are presenting? This is correct if it is.

Thank you. I am more looking for how it would look on a sentence tableau

It would help if you could mention what text you're using (I've asked you this a few times, but you haven't responded).

Generally, a sentence tableau is just the same as a truth tree - although a few texts treat sentence tableau much more modestly than a full-blown truth tree proof system. In any case, the notation for truth trees often varies from text to text. So, knowing the precise system would be useful in order to construct a tableau (i.e. tree) for your problem.

However, here is a truth tree. It may have a different format than what you're using. The lines aren't numbered below the argument. Note that when checking for validity using a truth tree, the negation of the conclusion is used in the tree. Also, you have "therefore" on line 2 and on line 4, but I'm instead assuming that you mean "if/then".

why the -S in line 5?

Did you read my post? Particularly this part:

Note that when checking for validity using a truth tree, the negation of the conclusion is used in the tree.

A truth tree is used to check for validity by conducting an exhaustive search for counterexamples. If none are found, the argument is valid.

So, the opposite truth value of the conclusion is used, in order to check if there are any instances where the premises are true and the conclusion false.

None were found here, so the original argument is valid.