Hey Jk,
Thanks for the question! I see you're working hard on Conditional Reasoning/Formal Logic--that's great!
Let me see if I can help you out with the example above.
The first thing we want to do is try to find a common term by which we can connect things, so let's take the contrapositive of G
A to get a -G (I'll use "-" for negatives, as you've done):
Contra: -A
-G
Now we can connect via the shared "-G":
-A
-G
-Q
Most people can get to this point without too much trouble. The questions becomes, "what can we infer from that chain?"
And the answer? Nothing. There are no inferences that we can make from that particular set of connections.
Don't worry about the "Not" idea for now; instead simply treat a "Not" group as an actual group. Now consider: all Not As are contained in the Not Gs group, and Most of those Not Gs are in the Not Qs group. Would there definitely HAVE to be any Not As in the Not Qs? Of course not. There could be 1 Not A total, which is in the group of 100 Not G. And of those 100 Not G, 60 (so Most) are in Not Q. But the 1 Not A does not have to be part of that 60, so Not A and Not Q do not have to be connected at all! Hence, no inference.
A few points in conclusion, then.
First, if you're seeing an answer key where -A
-Q is said to be correct, double check that you typed the inferences correctly here. Little typos/misreads can make a world of difference with this stuff.
Second, I realize that my explanation above probably sounds a little bit (or a lot) like Venn Diagramming. I do that only for the purpose of explaining the idea! Do NOT use Venn diagrams to represent these ideas on the LSAT, as they'll cause more problems than they'll resolve, trust me.
And finally, were the inference -A
-Q actually correct, then your point about
-Q
-A would, in fact, also be true. If most Not As are in the Not Qs, then certainly "some" are shared (i.e. "most" contains "some" by definition, and "some" is reversible so that if it's true for one condition it's also true for the other; I tend to simply think of it as "at least one shared").
I hope that helps - please let me know your thoughts if you get a moment!
Jon
