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Posted: **Sat Nov 16, 2013 9:52 pm**

I think the key here is that "nearly all" implies more than the bare minimum of most (51/100). Therefore, a "step down" in the logic ladder brings you to most.

Posted: **Mon Nov 18, 2013 12:04 pm**

BerkeleyMan5 wrote:Hey all,

I'm usually pretty good on formal logic and I generally only stick to the Powerscore (some and most) train methods when it comes to dealing with this kind of stuff.

I'm going through MLSAT LR right now and just looking over their formal logic section.

On one of the drill problems, it says:

"Nearly all of Jason's books are fiction books, and all of Jason's Book are written in Spanish."

I would diagram this like so:

JB--M--> F

JB-----> S

then I would combine these statements to get this.

F<--M--JB---->S

I would then reverse the most statement into a some statement and come to the conclusion that :

F<--S-->S

Some of Jason's books are fiction books written in Spanish (and vice versa).

However, the MLSAT book is claiming that "Most of Jason's books are fiction books written in Spanish" is a valid inference.

Intuitively this statement makes sense, but using the some and most train I don't see how you can safely get to this inference.
Is this a typo or is there some drastic error in my formal logic thought process? If any of you have the book this is on page 375, question 7.

I agree with you, I'm not a 180 lsater tho.
Even if it was F<----JB---->S instead of F<--M--JB---->S, you would come to the same conclusion.

soooooo... i'm not sure

Posted: **Mon Nov 18, 2013 1:45 pm**

The type of inference you're making is one which connects two elements and doesn't require the middle element to remain. FB <---S---> WIS is valid and means that some fiction books are written in Spanish (and vice versa). The inference in the book is really just restating two traits about Jason's books succinctly. We wouldn't be able to say anything like that if we took the term "Jason's books" out of the equation. For instance, we couldn't infer that "most fiction books are written in Spanish" or that "most works written in Spanish are fiction books."

If you were working with a real question, "Jason's books" would have to point to another element to use the inference that "most of Jason's books are fiction books written in Spanish." In a more likely scenario, "fiction books" or "written in Spanish" would lead to some third element. For instance, if we were given something like "all fiction books are written by individual authors" we could then infer that some works written in Spanish are penned by individual authors:
WIS <---S---> FB ---> IA

Posted: **Mon Nov 18, 2013 2:10 pm**

BerkeleyMan5 wrote:Hey all,

I'm usually pretty good on formal logic and I generally only stick to the Powerscore (some and most) train methods when it comes to dealing with this kind of stuff.

I'm going through MLSAT LR right now and just looking over their formal logic section.

On one of the drill problems, it says:

"Nearly all of Jason's books are fiction books, and all of Jason's Book are written in Spanish."

I would diagram this like so:

JB--M--> F

JB-----> S

then I would combine these statements to get this.

F<--M--JB---->S

I would then reverse the most statement into a some statement and come to the conclusion that :

F<--S-->S

Some of Jason's books are fiction books written in Spanish (and vice versa).

However, the MLSAT book is claiming that "Most of Jason's books are fiction books written in Spanish" is a valid inference.

Intuitively this statement makes sense, but using the some and most train I don't see how you can safely get to this inference.
Is this a typo or is there some drastic error in my formal logic thought process? If any of you have the book this is on page 375, question 7.

Diagrams are a useful tool, but you shouldn't be mechanical about them. You should always think about the things the diagrams represent. Let's say Jason has 100 books. All of them are in spanish. Nearly all of his books are fiction. Let's say nearly all is 95.

That means he has 95 fiction books. All of those 95 fiction books are written in Spanish, because ALL of jason's books are spanish.

Even if you thought nearly all just meant 'most' (51), this would still be true. Jason would have 51 fiction books, written in Spanish.

The formal rule is: "If you have an all statement, and a most statement that uses the sufficient conditional of the all statement, then you can combine them to make most statment"

A --> B
A --M--> C

Conclusion: Most of A are both B and C.

I say you shouldn't be mechanical, because if you actually imagined 100 books/cats/cars and attached a number to "nearly all", you could have figured this out on your own. That's how I learned this stuff, I just imagined real world examples I knew I couldn't get backwards.

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