[IMG]file:///C:/Users/user/AppData/Local/Temp/moz-screenshot.jpg[/IMG]Can you help how to establish the validity of the argument? (proof steps)
I am not sure it is valid. Consider the case when all variables except u are true and u is false.
And in general, what does one mean by "establish the validity of the argument"? There are so many ways to do it, from truth tables to formal proofs, and it completely depends on what instructor's plans for the course are. How were similar exercises solved in the past?
In fact, everybody knows what "and", "or", "not" and "implies" mean. So, even without knowing much technical details, you can try to come up with informal argument that either validates or invalidates the conclusion. Wrapping this informal argument into a form required by the course is often completely straightforward.
First, look at 8) in the solution. This is an assumption that came directly from the problem statement. However, there is a small difference
As I said, with this correction (in the problem statement) I believe the solution is correct. However, to claim that one knows the solution, I think one needs to be able to justify every step from 1 to 12. So, take a list of inference rules that you used in the course (or look at this Wikipedia page) and try to guess which rule is used in every step and to which formulas from previous steps it is applied. For starters, you can identify where the initial assumptions are used. E.g., as I said, assumption #3 (with a correction) is used in step 8. If you can't figure out which rule is used in some particular step, post here the rules and formulas for steps that you have figured out and the number of the problem step.