Setup and Rule Diagrams

[rahuldesarda]

In the last sentence, it is told to HANDLE THE LAST RULE WELL...
So this statement is intended for that particular game or is it always necessary to handle the last rule in a game like this?

[Adam Tyson]

That piece of advice applies to every rule in every game, rahuldesarda, but in the case of the rule referred to in that explanation it is especially important, because that is one of the most misunderstood rules in all of conditional reasoning. In fact, Dave recently re-posted an old blog article about that very type of rule, calling it "The Most Dangerous Conditional Rule on the LSAT". Here's that post:

https://blog.powerscore.com/lsat/the-mo ... -rule-lsat

Rules with a negated sufficient condition and a positive necessary condition, which can be read along the lines of "if not this, then that", mean that at least one of the two conditions must always occur. If the first thing is out, the second is in, and if the second is out, the first is in. Maybe they are both in - that doesn't violate the rule or its contrapositive - but they can never both be out.

Pay careful attention to that kind of rule, for when it appears you will have the opportunity to make a few key inferences and probably get one or two questions that become very easy as a result of your superior understanding.

Read Dave's post - you won't regret it!

[Mariam]

Hello- my diagram looked a little different. I didn't write out all the double not arrows, I made a large conditional connecting all the variables instead. My diagram looked like this:

W-->G-->NOT H-->NOT J-->S NOT S-->J-->H-->NOT G-->NOT W
or NOT M or M-->H

is this correct? am I missing something? is there an advantage to writing out all the double not arrows?

Thanks!

[Paul Marsh]

Hey Mariam!

Your formatting got a little messed up on your post but from what I can tell it looks pretty good, the only correction I'd make is that for your first chain, it should be "and NOT M" instead of "or NOT M" (remember that when we take the contrapositive of a conditional with multiple sufficient or necessary conditions, we need to change flip "and/or". Check out Lesson 2 in the Course Book for a refresher). Otherwise it looks good! I hope that conditional chain helped you attack this game well.

The advantage of drawing the double not arrows here is that you immediately realize that at least one of the two variables must be in the Out group. For example, from our first rule, we know that at least one of H or G must always be Out (they can also both be out). Double not arrows help us to visualize this inference. This can be very helpful for a question like #9, where our double not arrows allow us to quickly visually see that there must always be a couple of birds out.

Hope that helps!

[tetsuya0129]

Hi Powerscore staff,
While I was doing this game, the second rule (from the top) reminded me of another rule I had encountered:

If jays, martins, but not both are in the forest, then harriers are.

I am not sure how to correctly contrapose of this rule. I thought the contrapositive(s) would be:

~H J + M
&
~H ~J + ~M

Please help check whether my contrapositives are correct.
Thank you!
Leon

[Adam Tyson]

Hey Leon, great theoretical question! If the rule in this game had said "If J or M but not both are in the forest, then H must be in the forest," then the rule as originally written would be something like this:

J & M H

or

M & J H

The contrapositive would be:

H (J & M) OR (J & M)

Just change your "and" to an "or" and you have it! Obviously there is no way for J and M to both be in AND both be out, so the or just makes more holistic sense as well as being logically correct. That can be a little confusing, since we normally change "or" to "and" when doing the contrapositive, but we actually are doing that here. We are saying that "you cannot have J in and M out AND you cannot have M in and J out." That leaves the two possibilities here - they are both in or else they are both out.

Just to be clear, this is NOT the rule as given in this game! We're just playing a "what if" scenario to see how different rules might be handled in similar situations.

[leslie7]

Hi I realize someone asked something along these lines on this thread already but I'm wondering,

for this game I wrote out a large conditional as-well , I find it easier on my eyes to trace the connections like via a simple train-like fashion. After that, I'm able to create my double-not arrows.

I notice in the book they are disconnected rules (as in not linked together in a chain) and inferences are made based off them but I find that I spend more time having my eyes jump around trying to see the chained connections from one rule to the other (if that makes sense).

So generally, is it recommended to train ourselves to use the short, un-chained rules and look for inferences or is the chained-conditional just as fine , strategically speaking?

I guess I can train myself over time to link the rules in my mind much quicker but I do find it takes more effort on my part right now, as opposed to just linking them as I go along I find in my mind its more clear and I have a more fluid/rapid understanding of what triggers what.

[Dave Killoran]

So generally, is it recommended to train ourselves to use the short, un-chained rules and look for inferences or is the chained-conditional just as fine , strategically speaking?

I guess I can train myself over time to link the rules in my mind much quicker but I do find it takes more effort on my part right now, as opposed to just linking them as I go along I find in my mind its more clear and I have a more fluid/rapid understanding of what triggers what.

Hi Leslie,

This is a question where the right answer changes from person to person. Meaning, choose the method that works best for you. If you find that linking them all is fastest and clearest, by all means use that method! It's all about works best for you, and on a question like this there is no right or wrong way

Thanks!

[fleurgirl]

Hi there! I don't know if anyone has already covered this question here and I may be overthinking things, but for some reason I keep thinking that the rule S(strikethrough) J and it's contrapositive are then being used in Mistaken Reversals. Say we propose " If J is selected...". Wouldn't that mean that S could potentially be selected as well? Why is it assumed that one or the other MUST be present, but not both or both not be present? I hope that my question is clear... Thank you in advance!

[Ryan Twomey]

Hey Fluergirl,

So let me address your questions one at a time. I will list them.

1." If J is selected...". Wouldn't that mean that S could potentially be selected as well? "

Yes. If J is selected, S could be selected as well. If J is selected we don't know anything about S, so S could be in the forest or out of the forest. We don't know.

2. "Why is it assumed that one or the other MUST be present, but not both or both not be present?"

At least one of S or J must be selected. They could also both be selected.

At least one of them must be selected because if J is out, then S is in. Also if S is out then J is in. So no matter what, at least one of them must be in, because there is no way to place both of them out.

I hope this helps.

Best,
Ryan