The instruction of this question is:
Encode the following arguments and show whether they are valid or not. If not valid give countermodels i.e., truth assignments to the propositions which make them false.
If the investigation continues, then new evidence is brought to light. If new evidence is brought to light, then several leading citizens are implicated. If several leading citizens are implicated, then the newspapers stop publicizing the case. If continuation of the investigation implies that the newspapers stop publicizing the case, then bringing to light of new evidence implies that the investigation continues. The investigation does not continue. Therefore, new evidence is not brought to light.
My attempt:
Let $p$ denote "the investigation continues"
$\quad \space \space q$ denote "new evidence is brought to light"
$\quad \space \space r$ denote "several leading citizens are implicated"
$\quad \space \space s$ denote "the newspapers stop publicizing the case"
So, the premises are:
$p \to q $
$q \to r $
$r \to s $
$(p \to s) \to (q \to p)$
$\neg p$
$\therefore \neg q$
I am very much a beginner in logic so I am not sure if this is correct so far or how to prove or disprove this using the standard rules of inference. Any ideas?