Question Regarding Chapter 13 of LR Bible

[Callistio]

I’m very lost in the question #4 explanation despite checking the forums.

The explanation says that the first relationship that comes to mind is H <——/——> T but I don’t understand where this is coming from.

The premise chain is C <—-\——>T <—— P Conclusion is P<——/——-> H

So even if we were to do T<——P <——/——>H since we’re not supposed to start from a double not arrow wouldn’t it be T <—-some——>/H? When you add the premises from answer choice B it makes sense that H <—-/——>T but before that I don’t know where we would find this relationship.

Also, how come we can go “backwards” and infer that in an A ——> B that some Bs are As when contrapositive rules would tell us that /B——>/A when we are going backwards?

How do we go about actually using this in real questions? I found that I could do the practice ones in the book but then once I tried other ones it didn’t feel as straightforward. Is there a way we can practice so that we don’t have to draw everything out all the time? Some people say that it becomes intuitive but it gets super complicated sometimes

Thank you for your time!

[Jonathan Evans]

Hi, Callistio!

The explanation says that the first relationship that comes to mind is H <——/——> T but I don’t understand where this is coming from.

Given that all P are T (P T), the H T relationship would be the most direct way to justify this conclusion.

So even if we were to do T<——P <——/——>H since we’re not supposed to start from a double not arrow wouldn’t it be T <—-some——>/H?

Correct. All the Ps that are Ts are necessarily not H. So T H.

When you add the premises from answer choice B it makes sense that H <—-/——>T but before that I don’t know where we would find this relationship.

The key here is to figure out how you can get to T or T. What are your trajectories? Either way, you're satisfied.

Given the premises that:
C T
P T

To arrive at the conclusion that:
P H

You would be satisfied with:
T H
or
H C

because the latter implies
H T

so if H gets you to C, then you know you're not a T.

How do we go about actually using this in real questions? I found that I could do the practice ones in the book but then once I tried other ones it didn’t feel as straightforward. Is there a way we can practice so that we don’t have to draw everything out all the time? Some people say that it becomes intuitive but it gets super complicated sometimes

On a justify the conclusion question like this, the key is to notice the missing link and then ask how you can get there using the premises. If you know all your Ps are Ts and you know none of your Cs are Ts, then when they conclude none of your Ps are Hs, you recognize that the connection is going to involve connecting T and H. It would be great to do that directly as noted above, but barring that, if we can get from H to C, then we can infer correctly that Hs are not Ts and no P is an H.