I have been trying to understand how to use natural deduction rules to solve problems in logic. I understand the different rules, per se. However, I find it the most difficult to determine what can be set as assumptions, in order to solve the problems. For instance, I have understood the simple problems, such as the following: Where it is clear what ought to be the assumption and how to work from there.

Yet, when it comes to other problems, I get really confused as to what I am allowed to state as assumptions and what not to state as assumptions. Following is an example, in which I have stated R as an assumption, without knowing if that is "legal".

Is there a simple rule for proving formulas through natural deduction, with regards to problem solving techniques? For instance, when given problems such as:

How can I know which assumptions to make, etc.?

Any help is highly appreciated!