#feedback #typo

for the final sentence in this lesson, "For (C) to even be relevant, (C) itself requires an assumption that if students don’t get what they value, that will negatively impact their educationational achievement," there is a typo!

This also is confusing to me--I would appreciate clarification as well!

I may have figured it out--but if anyone can confirm this, that would be greatly appreciated!

For 9, because the chain is W --> M --> /LSD --> /H, but the actual premise is LSD (not /LSD), we have to contrapose /LSD (so it becomes LSD), and then we must go against the direction of the arrow (also contraposing, and those become the conclusions). So the conclusions are the contrapositives of what the arrow points away from: /W and /M.

For 10, the chain is W --> M --> /LSD --> /H once again, except this time, the premise /LSD is properly accounted for in the chain, meaning that it is not necessary to contrapose anything. As a result, to draw conclusions, you go with the direction of the arrow and take the conclusions as they are (i.e., do not contrapose), leading to the valid conclusion of /H.

Please let me know if this is the rule that I can use each time I need to draw conclusions from conditional chains: (1) that if you need to take the contrapositive of a chain, you contrapose the premises and then the conclusions are those that the arrow points away from and (2) if you do not need to take the contrapositive, the valid conclusions are those that the arrows point towards.

I have a question for the solutions to 9 and 10. I am confused about which "direction" you move on the chain to draw conclusions. How is the direction determined? Is it determined by by whether the link in the chain under investigation has a "/"?

For 9, I got:

W --> M

LSD --> /M

H --> LSD

LSD

Chained together: /W --> /M --> LSD --> H

When I looked at this chain, I thought about the relationship between "A --> B" : that A is a sufficient condition for B, and B is a necessary condition for A. The direction of the arrow confuses me when looking at the chain for some reason. Anyways, when I saw that the answer to 9 is /M and /W, I tried to start at the answer and go in reverse to figure out why this was the case. So I thought that given the fact that LSD is to the right of both /W and /M, then it is the necessary condition for them both (or, more specifically, that LSD necessitates /M, which necessitates /W).

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I thought I got it now and could move on to 10, but then I got stuck again. Here's what I had for 10:

W --> M

LSD --> /M

H --> LSD

/LSD

Chained together: W --> M --> /LSD --> /H

I tried to apply the same explanation that I thought worked for question 9 to this one, so I thought the conclusions were W and M. Then when I saw that the answer was actually /H, I tried to do what I did for question 9: start with the answer and work my way backwards to see if I could figure out the explanation. I thought that "A --> B" means that if A is true, B must be true. So maybe the question I am identifying as my area of confusion isn't the root of the problem, but part of a larger confusion and just the only way I'm noticing it. Because this question made me wonder why I should move with the arrows to draw conclusions as opposed to against them like I did in question 9.

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Putting my observations in 9 and 10 together, when the link in question does not have a "/", do you move against the arrows, and if it has "/", do you move with them? Is this a good rule of thumb or is this not actually how it works?

I would appreciate any replies, even if they're just guesses or people echoing my confusion. I get the group translation rules, I just struggle with chaining and drawing conclusions. I have gone over all of these formal argument/group translation lessons multiple times, but is there a specific one that points to my weaknesses and a way to improve?

Thank you