First, I separated out your second question in this post and made it into a new thread. We try to keep separate questions in separate threads so other students can find the answers easily
The other question is now at http://forum.powerscore.com/lsat/viewto ... =26&t=7340
Second, let's go back to the problem above. One of the best ways to figure out why Not Laws don't work is to place the variable in question into the position where it supposedly can't go. so, in this case, we'd place O into the Table 4. What happens then? Well, because of the other rules that connect to O, patrons would be forced into tables 1, 2, and 3. Ok, so far, that's not an issue. But, we know that one of the tables is also empty. That empty table has to go where? The only tables left are 5, 6, and 7, so it has to be one of those. But that's a violation of the rules too, and now we have a problem. Thus, the thing that started this all—O on 4—won't work.
It's a tough inference, but a classic "domino sequence" type of inference where a series of events is triggered by placing O on 4.
Please let me know if that helps clear it up. Thanks!