Double-Not arrow, Positive SUFF and Negative NECC, is it the

[masadatech]

This is from an excerpt from Page 15, Logical Reasoning Bible, after Chapter Five (the pages does not correspond, it is after page, 113, the page 15/30 [subsection of Chapter Five])

Under:

Rule #2. There is no traditional direction in logic

"Because of the fact that English speakers read from.....

diagrams here (on the real pages 15)

A --------> B <------|------> C

The texts on Page 15 reads:

"Each of the four diagrams contain identical relationship - and produce identical inferences - but they all look.....Yet, the underlying relationships are the same in each instances: all A's are B's and no B's are C's...

My question is this:

1. No B's are C's (is this an error?)

Should it not read, all B's are ~C's?

I am not sure. Please help.

Question 2:

I believe that

X -------> ~Y (If X, then no Y)
Y -------> ~X (if Y, then no X)

therefore, to combine, it will be same as saying

X <-----|-----> Y [double-not arrow]

possible outcomes:

1. X and no Y
2. Y and no X
3. possibly, neither X or Y

the "English" wording above (from your powerscore main point questions) says:

"no B's are C's"

recap:

A --------> B <------|------> C (original, from above)

"no B's are C's" (this means Negative SUFF and Positive NECC)

~B -----> C

contrapositive

~C -----> B

Is this still a double-not arrow relationship?

Please help.

reference:

powerscore lsat course, logical reasoning bible, "page 15" after chapter five: main point questions

[Jon Denning]

Hey msadatech,

Thanks for the questions and welcome to the Forum! Let me address these individually:

1. Sounds like you're asking about the possible distinction between "No B's are C's," and "All B's are not C's." Assuming I've understood the question correctly, the answer is that those are logically equivalent. That is, the B group and the C group have no members in common (no overlap). So either phrasing would be acceptable in describing that exclusion: No B in C group...similarly All B out of C group. That's a good example of how the test makers themselves can play with language (especially conditional language) to say the same thing in a variety of ways.

2. Things were looking really good for this second question--the inferences about X and Y and the possible outcomes--until I read this:

"no B's are C's" (this means Negative SUFF and Positive NECC)

~B -----> C

Here's the problem: "no B's are C's" is, as we just discussed, the same as "all B's are not C's." Now think about how you'd diagram that second version (B, not C).

It would be B NOT C ! The language of no B's are C's throws a lot of people off, but all it's telling you is that if you have a B, you know you cannot have a C.

So with it diagrammed correctly the chains tie together and (hopefully) it all makes sense!

I hope that helps!

Jon

[masadatech]

Hello Jon. Thank you so much for posting the reply. I feel very welcome. Thank you again.

I have a question to ask. On page 151 of the Logic Reasoning Bible, Question 2.

"Either Jones or Kim will win the election".

JWE = Jones wins election and KWE = Kim wins election

The correct answer is:

~JWE -------> KWE

I put down:

JWE -------> ~KEW

Where did I go wrong?

Question 6, Page 151

"It is either feast or famine"

F = feast and FAM = famine

I put F -----> ~FAM

This is incorrect. The correct answer is:

~F -------> FAM

It appears I am making the identical mistake over and over again. Please help. Why does it start with Negative SUFF instead of a Positive SUFF (sufficient) condition?

[Jon Denning]

No problem! Happy to help.

You, I'm afraid, have made a common assumption here in both cases that trips a lot of people up: you've assumed that if one occurs, the other cannot.

More specifically, we're not told that Jones and Kim cannot (somehow) both win, so diagramming it as JWE Not KWE would be a mistake. Instead, we only know that one of them MUST win, so if Jones loses (Not JWE) then we'd be sure Kim wins (KWE). That's why the diagram begins with the "not": the absence of one indicates the presence of the other.

Granted, it's difficult to imagine a scenario in real life where two people could win an election, or where you could have both feast and famine, but the point of these is to illustrate something that the test makers love to do, which is describe relationships and hope you make unwarranted assumptions.

Interestingly these set up like the 3-outcome situation you noted in your original question! You can have one, the other, or potentially both. What you can't have is neither, and that's why they're diagrammed with a "Not A B" construct.

Hope that helps!

[masadatech]

Hi Jon. I have a question for you.

1. If A ----> B, and If B ----> A

Q1. Is this basically A <------> B ? Meaning both (A and B) are "in" or they are "out" but never one in while the other out?

Q2. I am planning to take a formal logic course at a local college this Fall 2014. I was wondering if you had any suggestions as to which area to primarily concentrate on? I have a small child at home and the only person with an income right now. I am not taking the course for credits. The professor is allowing me to sit-in. So, I wanted to know if you have any suggestions for me to key-in/work-on some key aspect of the course so that I can be more successful with the LSAT.

Please reply at your convenience.

Thanks.

Phillip, Vancouver BC Canada

[Nikki Siclunov]

Hi Phillip,

Let me jump in here and add my 2c.

Regarding your first question, if it is true that A B, and also that B A, we can use the Double-Arrow to represent the bi-conditional relationship between A and B:

A B

In other words, either A and B must both occur, or else neither of them can occur: as you said, it's all or nothing. Your grasp of the bi-conditional relationship is spot-on.

Onto your second question: in my own experience, students who were exposed to formal logic before undertaking a test prep course with us seem to derive some benefit from it, judging from their performance in class and on their practice tests. However, there is always the question of whether such students pick up the concepts in class faster because they had taken a course in deductive or formal logic in college, or whether their natural predisposition toward logical thinking led them to excel at both college-level logic and in their LSAT prep studies. A classic causal dilemma, as you can surely see, but I'm willing to bet on the second hypothesis.

Second, the benefit of taking such formal logic courses is not as pronounced as you might expect. There are several reasons for this: first, the LSAT does not emphasize formal logic; on the contrary - test-makers have made a concerted effort (especially in recent years) to scale back the number of LR questions that would disproportionately benefit students who have been exposed to formal logic. These days, the LSAT emphasizes inductive reasoning (e.g. reasoning from a sample, probabilistic reasoning, analogical reasoning), logical fallacies, certain types of syllogistic logic, and - of course - conditional reasoning. You will never need to construct propositional proofs, know what a "truth table" is, or understand modal logic. I can count on one hand the number of LR problems over the past year requiring you to setup "some" and "most" diagrams. Ten years ago, there were a handful of those on each test.

Furthermore, some may argue that a course in formal logic would teach you to approach argumentation from a perspective that is too formalistic for the purposes of the exam, and not as attuned to the vagaries of language that test-makers have learned to exploit so well. You may develop a propensity to diagram every argument you see, which is neither sufficient nor necessary to get the questions right. In fact, as an approach it can slow you down, focus your attention on the wrong task, and ultimately make you less efficient. For instance, just because many of the arguments on the LSAT can be represented using Venn diagrams does not mean they should be represented in this manner. Accuracy need not come at the expense of efficiency. We teach you how to do both.

So, while I doubt you will derive a significant benefit from a course that focuses purely on formal logic, with the right attitude it shouldn't hurt. Pay attention to syllogistic logic ("some" and "all" statements), basic propositional logic (incl. conditional reasoning), and informal logic (incl. logical fallacies).

Hope this helps! Let us know how it goes

[masadatech]

Hello Nikki. Greetings from Vancouver, BC, Canada. Thank you for replying and posting. I have a question for you.

If the condition above were to be changed to "not A" then "B".

1. ~A -----> B
2. ~B -----> A

In this particular case, would it then become a "double-not arrow" scenario?

A <------|-------> B?

Thus, the result is either A will occur or B will occur or "neither" occur?

Please reply at your convenience.

PS: I am taking a deep breath and re-thinking about the course that I am thinking about auditing in September 2014 (formal logic course at the local college). Part of my thinking is that I continue to practice the LSAT and continue to read up on forum and study prep material geared towards the Dec 2014 test, and the other part says, it cant hurt and it is something I have been wanting to do in a very long time. Anyhow, I am sure more prayer and meditation would help with making the right decision. Thank you again for posting your reply. I really appreciate it.

PS2: For any one else reading this, I received a 143 on my first attempt back in Dec 2010, then I didn't study and thought to myself, why not, let's see how much you would drop, I left the second test (Feb 2011) with a prediction that I would drop 6-7 percent point. My forecast was accurate but the score sucked. LOL. I use these two scores to apply to three BC (British Columbia) schools; they all said no. Last year, I applied to eight (8) across Canada, all said no. So, as we say in my little outfit, suit up and show up and let the creator do the rest. So, that's what am doing. I realize now that for someone like myself (ESL background) half-measure test prep just doesn't cut it. I am studying close to 10 months to 11 months this time, practically 4-5 hours per day, five days per week, sort-of-like a job, and from this experience, I realize that I needed a lot more prep than I once thought I needed. I am aiming for a 151 and higher score this time. Oh, I applied under the mature/access/special access/discretionary category, cant help it, am an old cat and have been out of school for a long, long time. Anyhow, hopes my sharing of my own experience, strength and hope can help someone out there. If you are a local person (Vancouver, BC), and need materials to study but short on cash, I can perhaps lend you my materials when I am done. email: masadatech aaaaattttttttttt Hotmail doooootttttt coooommmmm LOL (attempting bot counter-measure here). Good luck with your LSAT Prep.

[Nikki Siclunov]

Hi masadatech,

Let me address your questions real quick:

If the condition above were to be changed to "not A" then "B".

1. ~A -----> B
2. ~B -----> A

In this particular case, would it then become a "double-not arrow" scenario?

The answer is no. A double-not arrow merely represents two conditions that cannot BOTH be satisfied at once. A B means that if A is selected, B cannot be (A ~B), and vice versa. By contrast, a statement in the form you suggest, where the sufficient condition is negated (~A B), requires that we select at least one of A or B (possibly both): if either one of them is NOT selected, the other one must be. If you wanted to use the double-arrow in this example, it would have to look like this:

~A ~B

In other words, if A is not selected, then it cannot be true that B is not selected. Due to the convoluted nature of this representation, we don't use it to represent relationships with negative sufficient conditions.

Good luck with the formal logic class (if you take it)! And don't worry about English being your second language. It's actually my third language... I found the TOEFL to be harder than the LSAT. The language of logic is, well... universal

[masadatech]

Hello Nikki. Thank you so much. I have stayed up nights on this topic alone. LOL

[Nikki Siclunov]

You're welcome! Also, losing sleep over this is entirely counterproductive

Good luck!