It is actually the word "few" which implies that "most are not"

Saying "some X are Y" means AT LEAST 1 member of set X intersects with set Y.

For instance, let's take the example statement that "some dogs are violent."

If 100% of all dogs on Earth were violent, would the statement remain true? Yes

50%? Yes

1%? Still yes

Even if literally ONLY ONE individual dog on planet Earth is violent? Yes!

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How do we negate the phrase "some dogs are violent?"

We say that NO DOGS (absolute zero) are violent. Or in another translation, "if you are a dog, then you are not violent."

Original: dogs ←s→ violent

Negation: dogs → /violent

To make a modification:

Y can actually represent "films that have survived into the 21st century" rather than just things in general.

That way, with #1, both the statements that "some silent films have survived into the 21st century" and "some films that have survived into the 21st century are silent" are logically true

assuming set X represents "silent films" and set Y represents "things that have survived into the 21st century," then:

#1 (X ←s→ Y) can be interpreted in two ways: "some silent films have survived into the 21st century" and also "some things that have survived into the 21st century are silent films."

#2 (X ‑m→ /Y) can be only interpreted as "most silent films (X) have not survived into the 21st century (/Y)."

With Rule #2, saying something like "few are" implies that "most are not"

original rule: predom-econ-trade → supp-pfp → benefits from absence of war

contrapositive (flip order & negate each): /benefits from absence of war → /supp-pfp → /predom-econ-trade

Yes, your example conclusion would indeed be valid when we consider the contrapositive.

For those confused about uni-conditionals vs. bi-conditionals, consider these:

Uni-conditional example: "You will receive a medal if you finish the race in first-place."

We can logically create this diagram: finish race in first-place → receive a medal

Steve received a medal. Can we logically conclude that he therefore finished in first-place? No! The rule only tells us what happens if people finish first-place. Perhaps people who finished second and third also received a medal. Maybe every race participant received a medal! Who knows?

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However, consider this bi-conditional example:

"You will receive a medal if and only if you finish the race in first-place."

The arrows now point both ways: finish in first place ↔ receive a medal

Christopher received a medal. Can we therefore logically conclude that he finished in first place? Yes!

(likewise, if we were just told that Christopher "finished in first-place," we could also logically conclude that he therefore received a medal).

Question #2 has two main concepts that we will play with:

1. "a railroad serves its customers well."

2. "it [the railroad] will not be a successful business."

The rule with "Group 3" is this: We can pick either concept, but we must both negate it and make it the sufficient condition (put it on the left side of the arrow). The necessary condition is the other concept LEFT UNCHANGED

As a result, we can create two sentences that are logically equivalent with the original sentence posed in the question.

1. If a railroad doesn't serve its customers well, then it will not be a successful business."

2. If a railroad will be a successful business, then it serves its customers well."

You're on the right track! To add a little more nuance, we can say:

Being a carrot is sufficient to being a vegetable, but not necessary.

Why? You don't need to be a carrot to be considered a vegetable. You could be broccoli or lettuce, for example. Nevertheless, if you are a carrot, you are automatically considered a vegetable.

Being a vegetable is necessary to being a carrot, but not sufficient.

Why? Just because you are a vegetable doesn't automatically mean you are a carrot. To be a carrot...you must be a carrot. Of course, if you aren't even a vegetable to begin with, like an apple or watermelon, there is absolutely no way that you could be considered a carrot