#2 - All cattle ranchers dislike long winters. All ski

[JKing]

CR- cattle ranchers
DLW- dislikes long winters
SRO- ski resort owners
LLW-likes long winters
L- lawyers


CR-> DLW
SRO-> LLW
LsomeCR

Therefore LsomeCR->DLW

and

LsomeDLW



(B)- No real correlation

(D)- incorrect reversal

(E) not necessarily true and the argument can't really prove it

Why is it not (A)? -- Some cattle ranchers are lawyers?

And why is it (C)? All lawyers are cattle ranchers

Did I just diagramm this wrong? I actually really contemplated (C), mainly because I just felt (A) was a little too easy of an answer. Then I thought I probably wrote it out wrong. Can you explain what it should look like? I also diagrammed it as

DLW and then instead of using LLW I just put DLW with a slash through it.

[Nikki Siclunov]

Your initial diagram is correct, although I would simply cross out "LLW" to designate "dislike long winters." Thus, we have 3 premises:

CR NOT LLW

SRO LLW

L CR

The conclusion we need to prove is contained in the question stem:

L NOT SRO

Before we do so, let's look at the three premises more closely. Since they all have conditions in common, we can connect them as follows:

L CR NOT LLW NOT SRO

The additive inference here is that some lawyers are not ski resort owners:

L NOT SRO

The conclusion we need to prove, however, is somewhat different. To prove that no ski resort owners are lawyers (i.e. no lawyers are ski resort owners), we need to turn this "some" connection into an "all" connection, i.e. into a solid arrow " ". To do so, all we need to say is that ALL lawyers are cattle ranchers (L CR). If that were so, the chain would look like this:

L CR NOT LLW NOT SRO

This chain proves the conclusion that L NOT SRO. Therefore, answer choice (C) is correct.

We cannot prove an absolute conclusion by adding a "some" statement into the mix of premises. This eliminates answer choices (A) and (B).

This is a classic example of a Formal Logic LR question. If you're enrolled in our Full Length course, this type of logic is discussed in the supplemental materials to Lesson 8.

Hope this helps!

[jcough346]

Can you explain why D is wrong?

[Adam Tyson]

I can do that, jcough, but first, take a look at the diagrams that Nikki provided and tell us how you would insert a diagram for answer D into that chain. Where would it go and what effect would it have? How would it go about strengthening the claim that no ski resort owners are lawyers? Give us your analysis, and we'll take a look and give you some feedback from there. Fair deal?

Talk to you more soon!

[biskam]

Your initial diagram is correct, although I would simply cross out "LLW" to designate "dislike long winters." Thus, we have 3 premises:

CR NOT LLW

SRO LLW

L CR

The conclusion we need to prove is contained in the question stem:

L NOT SRO

Before we do so, let's look at the three premises more closely. Since they all have conditions in common, we can connect them as follows:

L CR NOT LLW NOT SRO

The additive inference here is that some lawyers are not ski resort owners:

L NOT SRO

The conclusion we need to prove, however, is somewhat different. To prove that no ski resort owners are lawyers (i.e. no lawyers are ski resort owners), we need to turn this "some" connection into an "all" connection, i.e. into a solid arrow " ". To do so, all we need to say is that ALL lawyers are cattle ranchers (L CR). If that were so, the chain would look like this:

L CR NOT LLW NOT SRO

This chain proves the conclusion that L NOT SRO. Therefore, answer choice (C) is correct.

We cannot prove an absolute conclusion by adding a "some" statement into the mix of premises. This eliminates answer choices (A) and (B).

This is a classic example of a Formal Logic LR question. If you're enrolled in our Full Length course, this type of logic is discussed in the supplemental materials to Lesson 8.

Hope this helps!

Why can't we write out the first premise of CR NOT LLW as CR <--|--> LW instead? meaning CR double arrow w a bar in the middle LW?

Because all cattle ranchers dislike long winters, then if CR --> negated LLW. and by the contrapositive, if LLW --> negated CR... which brings me to CR <--|--> LW instead, meaning CR double arrow w a bar in the middle LW.

which is why I wrote out my condtl statement as: L <--some--> CR <--|--> LW <---- SRO

and I ended up getting the problem wrong lol

Would appreciate any help

[biskam]

My q points to a broader difficulty I have in formal logic q in using the proper negation... when to use x <--|--> y and x --> not y

[AthenaDalton]

Hi biskam,

You can diagram the statement "all cattle ranchers dislike long winters" any of the following ways:

Normal diagram: CR NOT LLW
Contrapositive: LLW NOT CR
Double line: CR LLW

In general, I prefer using the normal/contrapositive diagrams because they are easier to tag onto other logic chains.

To get to the right answer in this problem, once we know that all cattle ranchers dislike long winters and all ski resort owners like long winters, we can conclude that no person can be both a cattle rancher and a ski resort owner. From there, selecting answer choice (C) (all lawyers are cattle ranchers) leads us to the conclusion that no ski resort owner is a lawyer.

It all sounds a bit nonsensical when I write it out, but if there is no overlap between CR and SRO, and all lawyers are in the CR group, no lawyer can be an SRO.

I hope that helps clarify things for you. Good luck studying!

[biskam]

good to know--thanks!