Here is a question that's been bugging me:
"Derive the following, using the rules of natural deduction:
$$ \vdash \neg(P_{1} \rightarrow P_{2}) \rightarrow P_{1} \vee P_{2} $$
That is, give a derivation with no assumptions."
As the title suggests, I'm wondering if you guys have any general advice on how to play around with assumptions in these kinds of proofs? I often find myself struggling at the start, but once I'm convinced I have the correct assumptions, I can usually work through the question without too many issues. I'm particulary bad with negations, I tend to find...