Hi Rahul - thanks for the question! Let me run through some common situations that you see that reliably yield inferences, split up below by the types of games in which they typically appear. You'll see that primarily they result from repeated/connected variables between rules (although they don't have to, as there are other ways for variables to impact one another).
Note too that each of these is going to be something you will encounter (or have already encountered, depending on how deep into the LGB you are) over and over as you move through the book and subsequent problem sets and practice tests, so while this may be useful, I can't imagine it's going to pull back the curtain on any real LG revelations. We labeled them "classic," after all, because of how familiar they are
Linear Games
The most common rule-combination inferences in Linear games tend to result in variable-sequence chains, and produce Not Laws.
So rules like A ahead of C, and C and of F: A — C — F, with Not Laws at/near the beginning and end of the diagram for those variables.
Or a rule creating a block like B immediately before D, and then another rule placing a variable in a particular spot (G in 4, say). That gives Not Laws for B and D at the beginning (D not first) and end (B not last), but also around the position with the other variable in it: with G in 4, B can't be 3 and D can't be 5 in order to keep the BD block intact.
Grouping Games
Rule combinations in Grouping tend to produce either In/Out inferences, or Blocks/Not-Blocks (people together or apart).
For instance, if you had two conditional rules where A
B, and B
C, that would lead to A
C where A and C can't be selected together. So if you had C in then both A and B would be out, and if you had A in then B would be with it and C would be gone. [this is similar to the sequence chain discussed above, only conditional with arrows instead of dashes]
You can also sometimes draw additional inferences from two rules like those above, if you have a limited number of Out positions available. So imagine you only had two Out spots. Then B going out and taking A out with it (contrapositive of
A
B) is a really powerful situation, because it means C and all the rest would be In. Normally from just that connection of A
B
C you could have B and C both out together, but a limited Out group could yield further restrictions.
And of course rules with blocks can create required groups and impossible ones:
H and J are on the same team; K and J are also on the same team: that means H, K, and J all go together.
H and J are on the same team; K and J cannot be on the same team: that means K and J cannot go together either.
Three teams of three people each. H and J are on a team together. F and K are on a team together.
Inference? Those two blocks must avoid each other, as combining them would create a four-person group,
which is too many people.
So those are some of the more common scenarios you'll encounter with the big game types, Linear and Grouping. Obviously more exist—both new ones and subtle variations on the above forms—but hopefully that gives you a sense of how a handful of the most frequently tested work!
