In order, Blueballoon:.
1) In this instance, yes - if "most drivers are good drivers", that would disprove that the claim that most are NOT good drivers. That's the goal of negation. Don't do this on a "some" statement, though! "Some drivers are good drivers" does NOT negate the claim that "some drivers are not good drivers", because it's possible that both claims are true.
8) The negation of any conditional claim is done by showing that the necessary condition is not actually necessary, that the sufficient condition can happen "even if" the alleged necessary condition does not happen. We don't make a new necessary condition that is the opposite of the original one, but rather we just say that it is no longer necessary. In this case, and starting from your original translation of "We will not lose our rights
We protected our rights", the negation would look like this:
"We will not lose our rights
we may or may not have protected them - there's no way to be sure."
To put that another way, we might say "protecting our rights isn't necessary". Not that it IS necessary that we DID NOT protect them, as you diagrammed, but that protection is no longer a necessary condition when we do not lose our rights.
11) Nope, that would be making the same sort of error as I described in the case of "some" earlier in this post. "Many are aware" and "many are unaware" can both be true at the same time, so those claims do not negate each other! Many people read this forum and many do not; many people live in Europe and many do not; many cats have long hair and many do not, and so on. These are all possible simultaneously! "Many" is a relative claim, and it's almost impossible to put a number on it. It's more than one, certainly, but other than that we just can't tell. It's not like "most", where you know that it is more than half. In this case, the way to negate "many are unaware" is either to say "few are unaware" (because few is the opposite of many - you can't be both few and many at the same time) or else "not many are unaware."
Continue the good work! Good luck!
Adam M. Tyson
PowerScore LSAT, GRE, ACT and SAT Instructor
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