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Here is my long and hard work. I have worked over this question for hmmm more than over 2 hours.
I am not here to brag about it but I want you to listen to me and see if my logic is solid.

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19. At a gathering at which bankers, athletes, and lawyers are present, all of the bankers are athletes and none of the lawyers are bankers.

question: what must be true?

(I will only list two contenders which are C and E)

C: some of the athletes are not lawyers
E: None of the lawyers are athletes.

the correct answer is C.

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I have read some explanations online and the almost equivocal explanation is that some of the athletes are bankers and bankers are not lawyers
so C is correct!.

However, this really bothered me since the explanation makes sense but cannot mechanically, systematically reproduced
when there is a similar question like this.

Here is my reasoning and I want you to be the juries how logically sounding my method is.

First, "all of the bankers are athletes" must not be translated as Bankers -> Athletes.
This diagramming robs the complexity of this question since quantifiers are used.

Second. "all of the bankers are athletes" must be All Bankers -> SOME athletes.
Here me out why I diagrammed it as "SOME athletes" a quantifier not introduced in the stimulus.
Some means anything but nothing.

"All of the bankers are athletes" is ambiguous sentence. All bankers can be all athletes. All bankers can be few athletes. All bankers can be many athletes etc.
Quantifier some pretty much encompass all of these ambiguity.

Therefore my diagramming

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All Bankers -> Some Athletes
None Athletes -> Not All Bankers

None Lawyers -> Some Bankers
None Bankers -> Some Lawyers

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Now, by the formal logic, an equivocal, beyond the doubt logical chain must be provided to be
an answer for MBT question type.

Answer choice (E) says "None of the lawyers are athletes"

None Lawyers -> Some Athletes.
None Athletes -> Some Lawyers.

Now, there is absolutely no way to prove this my forming a logical chain using the information above.
So, E is cannot be proven and may or may not be true.

However, look at (C)

"Some of the Athletes are not lawyers"

Some Athletes -> None Lawyers
Some Lawyers -> None Athletes.

Using the information provided by stimulus

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All Bankers -> Some Athletes
None Athletes -> Not All Bankers

None Lawyers -> Some Bankers
None Bankers -> Some Lawyers

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All Bankers -> Some Athletes -> None Lawyers -> Some Bankers.

Of course, All bankers must be some bankers because All includes some.

Lets loot at the contra-positive of C

Some Lawyers -> None Athletes

None Bankers -> Some Lawyers -> None Athletes -> Not All Bankers.

No 0 number of Bankers are not all Bankers.

If there is no cookies on the tables, of course not all the cookies are on the table since
None includes not all.

What do you guys think about this?

Jun

Just took this one today. You're overthinking it way too much.

The premise starts by saying there are bankers athletes and lawyers present. So that means there is at least one banker, which means there is at least one banker/athlete.

Being a banker is sufficient to be an athlete, but there is nothing to diagram that links athletes to lawyers.

you have

Banker --> Athlete

Lawyer <-/-> Banker

The only inference you can take from this is ~athlete --> ~banker

E is incorrect because there is no inference that implies this.

C is correct because you know there is at least 1 banker/athlete present, who can't be a lawyer.

I think that you might be overcomplicating this a little bit.

I missed this the first time that I did this PT, as well. However, I narrowed the answer choices down to both B and C.

B) Some of the Lawyers are not athletes.
C) Some of the athletes are not lawyers.

You can write the stimulus down like this:

All of the bankers are athletes. B---->A
None of the lawyers are bankers. L=~B or ~L=B (the latter works better in this situation)

~L=B--->A

This last logical statement can be deconstructed to read that "some athletes are bankers and are, therefore, not lawyers." As it is, some athletes are not lawyers. The mistake that I made, initially, was to reach out of the scope of the argument-- the logic presented gave us no information as to whether or not the lawyers could be athletes. We cannot assume that there are lawyers who are athletes or that no lawyers are athletes; the stimulus simply does not supply us with enough information.

My conditionals were:

B-->A

~A--> ~B

L --> ~B

B---> ~L


Of those I looked at the conditions which shared the same sufficient (Remember Sufficient --> Necessary is how conditionals are written). That would be the below two:


B-->A

B---> ~L



In my class, we are taught to look for similar sufficients in our conditionals to make deductions between the necessary statements. In this case, if all Bs are As and all Bs are not Ls, can we make some deduction from this? Yes, we can. We can safely assume here that some As (some = at least 1) are not Ls (and vice versa).

That leads us to answer choice C. When it comes to conditional statements, look for similar sufficient to make your deductions.

omg mrizza thank you for the input.
that was really helpful.

Hello,

Some tips on this question for future test takers.

First, I would not suggest approaching this question using conditional reasoning since it won't reveal the correct answer. Instead, I recommend using Venn Diagrams - a tool of categorical reasoning.

1. Draw three circles with an overlapping center
(it should look like a clover, see https://media1.britannica.com/eb-media/ ... 28CE41.jpg and ignore the shading and comments beneath).

2. Label each circle with one of three letters "B", "L" or "A"

3. For the statement "All bankers are athletes", shade any area of circle "B" that would not include "A"

4. For the statement "No lawyers are bankers", shade whatever remaining area there is between circles "B" and "L" (i.e, they should not intersect)

You'll notice a tiny space left between B and A that is left unshaded.

If we assume that bankers and athletes exist - which is usually assumed on the LSAT, and hinted at in the beginning of the passage for this question, it would mean that at least one banker is an athlete. This is the same as saying at least one athlete is a banker, or "Some athletes are bankers".

5. Jot an "X" in the unshaded space where "B" and "A" intersect

You will notice that the "X" does not overlap with lawyers. This means "There exists at least one banker/athlete who is not a lawyer".

This is found in answer choice C, "Some (at least one) athlete(s) are not lawyers".