Sorry, I am just preparing some notes for my students and want to double check I have my facts right before I give the notes to them. So these are my premises:
- $\lnot p\rightarrow o$
- $s\rightarrow r$
- $\lnot (o\land r)$
- $\lnot p$
And I want : $\lnot s$
So, casually, we can get from $\lnot p$ to $o$ using Modus Ponens, proving $o$.
$\lnot(o\land r)$ is the same as $\lnot o\lor\lnot r$.
Using simplification we can assert from this that ¬r is true.
From this we can get to $\lnot s$ using Modus tollens.
Is this correct ? I am tired from writing ~40 pages of notes and am nearly positive I have missed something here.