I have been trying to understand how to use natural deduction rules to solve problems in logic. I understand the different rules. 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.
However, 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:
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!
I'm still a bit confused as to what I can set as the assumption(s).
The below example confuses me. In line (I), both the first conjunction [(P->Q)&(R->Q)] of the expression, as well as the second conjunction, [P & R], which is actually the conclusion of the left-most implication, is also set as an assumption.
As @Henning Makholm explained, I expected to end this proof with two stacked →Is.
The problem is how to know what expressions to use as assumptions? I keep seeing worked examples, all of them which make sense. However, when I am to solve problems myself, I get confused with the assumptions that can be made. Any advice on this particular matter?
For instance, I thought one could not assume an expression that is also the conclusion of an implication (P & R), as an assumption? Or is this just the case of the right-most conclusion, in this case Q?
Evidently, the choice of assumptions confuses me!.