Hi Grace - thanks for the question and welcome to the Forum!
That's a great question you've asked, and a concept (chains/linkage) that'll you'll definitely see tested in both Logical Reasoning and Logic Games, so I'm glad you took the time to post here
To me, one of the most critical ideas in conditional reasoning, whether it's an individual relationship like A
B or a chain like A
B
C, is recognizing the things that MUST be true, that merely COULD be true, and that absolutely CANNOT be true from the information you're given.
Here's what I mean, working off a slightly-shortened version of the lengthy chain you've provided (the concepts will be clear with a smaller chain, and save me some typing
).
What must be true if we know that A
B
C
D is true?
Well, first, we'd know that A gives us B, C, and D for sure! We can follow our arrows from left to right, from A on down. Similarly, we'd know that if we have B we also have C and D, just following the arrows down the chain from B. And if we have C? Then we for sure have D, since C points right to it!
Other things can be known as well, and we call these contrapositives. They're what occurs when required/necessary pieces in a relationship go away. The outcome? Whatever depended on those necessary pieces must go away, too.
So what does A depend on (point to) here? It requires B, C, and D! So if we lose any of those then A is out as well! What does B require? C and D. So if C or D is gone (or if both are gone), then B is out too. And C? C depends on D being there...so if D is gone then C must be gone too.
That's very frequently tested in conditional reasoning, particularly with chains, so make sure you can see inferences directly (from A, or B, etc) and consequently (from the absence of a required piece, triggering the contrapositive).
Alright then, that's all the things that we can know as "must" here. But what about the opposite end of the spectrum? What are things that CANNOT be true? These would be the "not consistent with the chain," as you've nicely phrased it.
The "cannot" ideas here are the exact opposites of the "must" relationships/outcomes we just discussed. So for instance it cannot be true that if A is present B, C, and/or D are gone. A without B (or C or D) is impossible, so saying A alone, or the group consists solely of A and D, for example, cannot be correct. Put another way: what would deny the truths we've established? Well B without C would break the chain, so it cannot be true. And so on.
So there are a fair number of truths, affirmative and negative, that we can know from that chain.
But what about uncertainties? What's merely possible, but not guaranteed (true or false) from the chain?
The answer is two-fold, and boils down to the two classic conditional mistakes that Lesson 2 presents: Mistaken Negations and Mistaken Reversals.
Negation errors occur when you're missing the sufficient (beginning of arrow) piece and still try to go somewhere. You can't. If we don't have A, for instance, we never start the chain in the first place and so we can't know anything else! A gone? B, C, and D might be there or they might not. No way to know, so no inferences are possible from A's absence.
B gone? We then we can't follow the chain from B to C and D, because we don't have B to trigger it! But we CAN know that without B being there then A can't be there either (contrapositive), so there's a single inference from no B: no A. But that's it.
Reversal errors are similarly problematic, and for the same reason: they treat possibilities as certainties. That is, B tells you something about C and D because you can follow your arrows to them. But what does B tell us about A?? Nothing! It simply allows A to be possible. But nothing is guaranteed: A can still come and go as it pleases, because B doesn't point to it. To go from B to A would be to move in reverse, against the arrow, and that causes all kinds of problems.
In short, A and B together can be known if A triggers it. But it's merely a possibility, and unknowable, if B is the trigger. So never, NEVER move in reverse! It's the most common (and most tempting) trap and it's crucial that you learn to avoid it!
So that's conditional inference making in a nutshell! Just be sure to avoid confusing possibility (Negations and Reversals) with certainties (direct inferences and contrapositives) and you'll be just fine
I hope that helps!
