Grouping Setup Practice Drill #2

[Dave Killoran]

Hey Katya,

Let's walk through what happens when L is offered, showing each step and then what we know about the variables occurring and not occurring:

• 1. L is offered.
  
  Variables: L
  
  
  
  2. From the second rule, E is offered, and M is not
  
  Variables: L, E, M
  
  
  
  3A. When M is not offered, nothing happens as a consequence. No change in variable status.
  
  Variables: L, E, M,
  
  
  
  3B. When E is offered, we know that causes a problem in the first rule, namely that A cannot occur. We don't know anything about F though, because it's just floating there in the necessary condition.
  
  Variables: L, E, M, A
  
  
  
  4. When A is not offered, we know that causes a problem in the third rule, and it enacts a contrapositive where both sufficient conditions cannot occur.
  
  Variables: L, E, M, A, O, S

So, the thing about F is that we don't know what's occurring there. It either can or cannot occur. The trick is seeing how F and E are just two necessary conditions, and when one of them doesn't happen, it doesn't have an impact on the other. For example:

• To get into the club, you must be rich and famous.
  
  
  Rich
  Club      +
  Famous
  
  Let's say Maria is not famous. We know then via the contrapositive that she's not getting into the club. But does it tell us anything about whether she is rich? No, not at all, and that's just like F here

Please let me know if that helps. Thanks!

[Katya W]

Hey Katya,

Let's walk through what happens when L is offered, showing each step and then what we know about the variables occurring and not occurring:

• 1. L is offered.
  
  Variables: L
  
  
  
  2. From the second rule, E is offered, and M is not
  
  Variables: L, E, M
  
  
  
  3A. When M is not offered, nothing happens as a consequence. No change in variable status.
  
  Variables: L, E, M,
  
  
  
  3B. When E is offered, we know that causes a problem in the first rule, namely that A cannot occur. We don't know anything about F though, because it's just floating there in the necessary condition.
  
  Variables: L, E, M, A
  
  
  
  4. When A is not offered, we know that causes a problem in the third rule, and it enacts a contrapositive where both sufficient conditions cannot occur.
  
  Variables: L, E, M, A, O, S

So, the thing about F is that we don't know what's occurring there. It either can or cannot occur. The trick is seeing how F and E are just two necessary conditions, and when one of them doesn't happen, it doesn't have an impact on the other. For example:

• To get into the club, you must be rich and famous.
  
  
  Rich
  Club      +
  Famous
  
  Let's say Maria is not famous. We know then via the contrapositive that she's not getting into the club. But does it tell us anything about whether she is rich? No, not at all, and that's just like F here

Please let me know if that helps. Thanks!

Wow, thank you Dave, I appreciate that rule by rule walk through! I was able to come to understand how L being offered meant A, M, O, S could not be offered. But I wanted to show myself how F could be offered if L was too. But basically, for what I understand from your diagram and analysis, and what you said in the end, is that we don’t really know.

F is a mystery and the only reason it is the right answer is because all of the other answers were wrong! Haha. So I guess I have to live with that sometimes an answer is the best answer because all of the other ones must be false?

Thank you Dave!!
Katya

[Dave Killoran]

F is a mystery and the only reason it is the right answer is because all of the other answers were wrong! Haha. So I guess I have to live with that sometimes an answer is the best answer because all of the other ones must be false?

Great, glad I could help! But F is correct because it meets the criterion in the answer choice

The question stem says, "If law is offered, then each of the following must be false EXCEPT"

Which is the same as "If law is offered, then each of the following cannot be true EXCEPT"

Which is the same as "If law is offered, then which one of the following could be true"

And in this case A, M, O, and S each cannot be offered with L, but F could be, so F is the correct answer

Ultimately, you can say either that F is the only answer that meets the criterion, or that the other 4 don't. Either way gets you there!

[Katya W]

Great, glad I could help! But F is correct because it meets the criterion in the answer choice

The question stem says, "If law is offered, then each of the following must be false EXCEPT"

Which is the same as "If law is offered, then each of the following cannot be true EXCEPT"

Which is the same as "If law is offered, then which one of the following could be true"

And in this case A, M, O, and S each cannot be offered with L, but F could be, so F is the correct answer

Ultimately, you can say either that F is the only answer that meets the criterion, or that the other 4 don't. Either way gets you there!

Thank you Dave!! Your further explanation helped clarify it even more for me. I realized a little too late that I said “must be false” in my previous post, but what I meant was “must be incorrect”. And when I said “wrong” in the post earlier I meant “incorrect” as well! I have to start being careful with how I use my terms now.

Thank you though, you really helped me understand that F was the correct answer because although we don’t know what it’s doing in relation to L, it “could be true”, and since the others “cannot be true”, it comes out as the correct answer.

I appreciate your work and your help!

[med2law]

Hello, I solved this problem using a different method than the book. I wanted to make sure this method is OK, despite it giving me the correct answer. Below I have shown my work. Thank you for any feedback!

A F+E
contrapositive:
E or F A
(meaning, E A because E is sufficient alone for A)

L E+M A O+S

Therefore, it's quickly obvious that either economics or finance could be offered if law is offered. Only finance is a choice, so I select (B) Finance. I know the E + M portion above seems to imply that if E + M then A, but I didn't worry about that because E alone is sufficient for A, so I went ahead with the chain and it gave me the right answer.

Is this a safe approach? Could I represent it differently to avoid the connotation in my diagram, which seems to infer that E + M (and not just E) indicates the necessary condition A occurs? Because A doesn't really care about M.

If this makes any sense, your feedback would help a lot. Thanks once more!

[Jeremy Press]

Hi med2law,

You're dead on with this one! Really nice work.

Here's how you could represent your chain to avoid the trap you're talking about:

Screen Shot 2020-08-28 at 4.45.58 PM.png

The problem you're trying to avoid is the primary reason we recommend diagramming two (or more) necessary (or sufficient) conditions vertically rather than horizontally.

I hope this helps!

[Dave Killoran]

Hi Med,

Thanks for the question!

Since this is ultimately a Could Be True question, what you did was simply note that F had no violation with L, and thus it could occur. That's totally reasonable However, for most students that doesn't suffice as a reasonable explanation (which makes sense; you can't explain the answer to a Could question by simply pointing out that it's possible to have happened ) and so we make sure to show why all the wrong answers can't occur. But that's really different sides of the same explanatory coin, if that makes sense!

The diagram you made suffers in that it attempts to put everything on one line. This is great when all the relationships are single conditions, but that's not what happened here. So, instead use something like what Jeremy posted for you that separates the various conditions vertically, which will be clearer and reflect exactly which variables are connected.

Good job!

[med2law]

Thank you both! This answers my question. The vertical tip is great.

[Garrettgregor]

I'm having trouble getting to the last inference on page 330:

O
or L
S

How does one logically make this inference?

[Jeremy Press]

Hi Garrett,

That's coming from a tricky combination of all three rules!

Start with the last rule:

O
or A
S

Now add (part of) the first rule:

O
or A E
S

Now add (part of) the contrapositive of the second rule:

O
or A E L
S

With that chain in place, the middle two steps can be skipped over, yielding the double-not arrow relationship:

O
or L
S

Another way to arrive at that same inference is to observe, as the explanation does, that A and L have opposite necessary conditions. A requires NOT E. L requires E. Two things that have opposite necessary conditions cannot be together. So A and L cannot be together, i.e. A L. Given that, from the last rule, O or S requires A, that means O or S also cannot be with L, hence that final double-not arrow inference.

Let us know if that clears it up for you!