“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend.”

P1: Friends ‑m→ Wizards

P2: /Friends ‑m→ /Wizards

C: Draco Malfoy (Wizard) → Friend

versus…

“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is Harry Potter's friend, is probably a wizard.”

P1: Friends ‑m→ Wizards

P2: /Friends ‑m→ /Wizards

C: Friend → Draco Malfoy (Wizard)

I think I see how negation is key here (someone correct me if I’m wrong).

For example, if we take the statement…

"All Jedi use the Force" and negate it, we get "Some Jedi don't use the Force.”

Original: J → F

Negated: J ←s→ /F

This shows that it's possible for someone to be a Jedi without using the Force. So, going back to the original argument:

"All Jedi use the Force. Count Dooku uses the Force. Therefore, Count Dooku is a Jedi."

It is invalid because it’s possible that some Jedi don't use the Force. It is not enough evidence to say Count Dooku is a Jedi just because he uses the Force.

So, technically, we aren't wrong in our translation process for the argument:

“All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter.”

Birds → Migrate South in Winter

Monarch Butterfly → /Bird

Monarch Butterfly → /Migrate South in Winter

It seems that what makes this conclusion invalid is that it's assuming monarch butterflies don't migrate south in the winter simply because it's not a bird. So, it's not that our process is wrong, but rather that we're missing additional premises that would support the conclusion. We're making an assumption that isn't justified by the given information. All ≠ Only.

“No student is chosen for Gryffindor unless they exhibit bravery. Therefore, if a student exhibits bravery, they will be sorted to Gryffindor”

I followed the Group 3 and Group 4 conditional indicator rules and got:

Premise: must Exhibit Bravery → to be Chosen for Gryffindor

Conclusion: all Exhibit Bravery → will be Chosen for Gryffindor

It took me a while to understand why the conclusion is invalid. I added the words "must" and "all", and also "to be" and "will be" to my lawgic translation, because it helped me see what the sentences were actually saying. The conclusion is invalid because it's claiming that anyone who's brave will be a Gryffindor (are there not brave people in the other houses?), whereas the premise is saying that to be a Gryffindor, you have to be (at least) brave. That's a big difference. My only concern is that I didn't catch this initially, and it took me some time to realize it. It would be really helpful to have a strategy to avoid getting tripped up on these kinds of questions.

All water has flavor (A → B)

Most water has minerals in it (A ‑m→ C)

Therefore, some flavor comes from minerals (B ←s→ C)

Negated:

Some water doesn’t have flavor (A ←s→ /B)

Most water don’t have minerals in it (A ‑m→ /C)

Therefore, all/no flavor comes from minerals (B → C)

some, all, some

Some water have minerals in it. All minerals give water flavor. Therefore, some water has flavor in it.

Water ←s→ minerals

Minerals → flavor

Water ←s→ flavor

Negated:

Water → minerals

Minerals ←s→ /flavor

Water → flavor

All or no water has minerals in it. Some minerals don’t give water flavor. All or no water has flavor in it.

most, all, most

Most water have minerals in it. All minerals give water flavor. Therefore, most water has flavor in it.

Water ‑m→ minerals

Minerals → flavor

Water ‑m→ flavor

Negated:

Water ‑m→ /minerals

Minerals ←s→ /flavor

Water ‑m→ /flavor

Most water doesn’t have minerals in it. Some minerals don’t give water flavor. Most water doesn’t have flavor.

most, most, some

Most water have minerals in it. Most minerals give water flavor. Therefore, some water has flavor in it.

Water ‑m→ minerals

Minerals ‑m→ flavor

Water ←s→ flavor

Negated:

Water ‑m→ /minerals

Minerals ‑m→ /flavor

/Water → flavor

Most water doesn’t have minerals in it. Most minerals don’t give water flavor. No water has flavor.

Question 3 I had:

If more than three inches of snow accumulate, then classes will be canceled.

3+ in snow → classes canceled

3+ in snow ←s→ /classes canceled

If some (at least 1 in) snow accumulates, then classes will not be canceled

How come question 2 wouldn’t be negated as /Alphabets → Phonetic or no alphabets are phonetic? I thought some negates to none.

It would've been nice to get an explanation on the difference between a contrapositive statement and a negated statement because I was wondering why we can't just say:

"To be a Jedi, one must be able to use the Force."

J → F

"If you don't know how to use the Force, you are not a Jedi"

/F → /J

but I realize that we just need to negate the sufficient condition for “All” conditional statements, correct?

"To be a Jedi, one must be able to use the Force." Translates to "All Jedis must be able to use the Force."

“It's not the case that all Jedis must be able to use the Force”

/J → F

Something that helps me with these new quantifiers, and may click as well for those who have written literature reviews, is the distinction between "most", "many", and "some" when referencing scholarly opinions. I try to reserve "most" for when I'm describing a viewpoint that is widely accepted by the majority of scholars. For instance, when I say "many/some scholars argue that", I'm implying that a number of scholars hold a particular view, but not necessarily the majority. On the other hand, when I say "most scholars argue that", I'm suggesting that the majority of scholars agree on that point.

“Many scholars argue that 7sage should incorporate videos to help illustrate difficult concepts and enhance the learning experience. Some scholars, however, defend 7sage's current approach, suggesting that they are doing their best with the resources available. Nevertheless, most agree that, given the premium they pay for the service, they should have access to high-quality visual content that meets their expectations.”

I'll be happy with a good score, doesn't have to be 170+. I hope everyone here studying hard will get great scores as well <3.

Question 5

“When knowledge of the existence of a particular fact is an element of an offense, such knowledge is established if a person is aware of a high probability of its existence, unless he actually believes that it does not exist.”

Translation: For something to be an offense, the person who committed an offense has to be aware they committed an offense, unless they actually believe they didn’t commit an offense.

Rule: For something to be an offense, the person who committed an offense has to be aware they committed an offense

Considered offense → aware of offense

Exception: unless they actually believe they didn’t commit an offense.

Disbelief → not considered offense

Contrapositive: If someone is not aware of them committing an offense, then it isn’t considered an offense. It would be considered an offense, if someone actually believed they committed an offense.

Couldn't we just simplify it to:

"All residents of The Beresford are prohibited from keeping pets in their apartments unless the animal serves a legitimate medical purpose."

Residents prohibited from keeping pets → animal doesn't serve a medical purpose

Contrapositive: If animal serves a medical purpose, then resident is not prohibited from keeping a pet.

I take the arrow as the rule. Written this way, it’s clear that if you're not a resident, the rule doesn't even apply to you - you're not even in the picture/domain. And if your pet isn't serving a medical purpose, you're out of luck - no pets allowed in the building.

Is it possible to get the same outcome if we were to smush all the sufficient conditions together? For example:

“All New York City residents living in buildings with more than ten units have an inalienable right to keep a pet if that animal has been kept openly and notoriously for three months or more.”

NYC 10+ unit apartment dwellers with pet openly and notoriously kept for 3+ months → inalienable right to keep pet

Contrapositive: You don’t have an inalienable right to keep a pet if you are not a NYC 10+ unit apartment dweller or pet owner who has openly or notoriously kept an animal for 3+ months.

Omg. I literally wrote down "self-cooked pastry" and "birds singing" because that's what the formula led me to, even though it sounded crazy at first. I didn't know how to articulate it in English, so I just scribbled it out. I came to this conclusion by referring back to the formula, labeling:

real magicians (A) → self-cooked pastry (B)

birds singing (C) → real magicians (A)

…which left me with the combination of B and C as the only possibility.

Conclusion: self-cooked pastry (B) → birds singing (C)

I see how this can trick people because we read between the lines normally. But this test wants us to play it straight and just think with what we are told and given only, without implying anything else.

So, is there such a thing as a true necessary condition, or is this exercise mainly about understanding the prompt, since we can turn any condition into a necessary one just by negating it when these specific indicators are present?

I had it written as:

Immutable trait → Suspect class

And since plaintiffs didn't show any evidence of past rulings on homosexuality being an immutable characteristic, then they failed to show they are in a suspect class.

Vegans don't eat meat. If John eats tofu every time I see him at lunch, then he must be a vegan.

Eating tofu → Being vegan

Vegans don't eat meat. If John wasn't a vegan, then he would not eat tofu every time I see him at lunch.

Not being a vegan → Not eating tofu

Did I get that right?

I feel like that kid who snuck into the deeper side of the pool, holding onto the rail for dear life. Math and Lawgic are definitely not my strong suits lol! I'll just have to stick to the "English" versions of arguments.

Right now, I’m drinking Yerba mate, a subset of tea, which is a subset of beverages.

If we're just looking at Yerba mate and tea, Yerba mate is the subset/sufficient condition, and tea is the superset/necessary condition. Similarly, when looking at tea and beverages, tea is the subset/sufficient condition, and beverages is the superset/necessary condition.

I don't have to be drinking Yerba mate to be drinking tea (sufficient). But if I am drinking Yerba mate, then I'm definitely drinking tea (necessity).

Therefore, all dogs are cute!

It seems like these last lessons are highlighting that we don't just exist in a vacuum, and when we're presented with a supposed cause-and-effect relationship, such as:

No visual explanations for concepts → Confused

We should consider that there might be other factors at play. In this case, confusion could stem from various reasons beyond the lack of visual explanations. For instance, I’m neurodivergent, which could be an alternative hypothesis for many of us who are confused. It's also possible that some 7Sage users might attribute their confusion to the lack of visual explanations simply because they've been influenced by comments from other 7Sage users.

So, is the main takeaway that we should be cautious of given cause-and-effect relationships and look for ways that the world of the text may influence the given cause and effect, and then consider alternative hypotheses?

I'm a visual learner, and I'm having trouble understanding the material. I've reviewed it multiple times, but I still don't get it. In previous lessons, the material included visual explanations, and I was able to understand the concepts without difficulty. Now, the material doesn't include any visual explanations for these new concepts. Other 7Sage subscribers have also complained about the lack of visual explanations and have reported feeling confused.

Assumed Causal Relationship: No visual explanations → Confusion/lack of understanding

Hypothesis 1: A causes B

The lack of visual explanations (A) causes confusion (B).

Hypothesis 2: B causes A

Confusion (B) causes the lack of visual explanations (A).

Hypothesis 3: C causes both A and B

Laziness (C) causes both no visual explanations (A) and confusion (B).

Hypothesis 4: Just a coincidence

There is no causal relationship between the lack of visual explanations (A) and confusion (B); they are just coincidentally related.

Evaluation:

Chronology: Hypothesis 2 is out because the lack of visual explanations came before my confusion.

Causal Mechanism: Hypothesis 3 is weakened because I reviewed the material multiple times, so I can’t be that lazy (but 7Sage, wya? lol)

Similar Causal Relationships: Hypothesis 1 is strengthened because other 7Sage subscribers are also reporting feeling confused due to the lack of visual explanations. It's not just me.

Direct Evidence: Hypothesis 4 is out because I'm a visual learner, and I need visual explanations to understand the material. Surely, it isn’t a coincidence that I’m confused.

Prediction: If I get visual explanations, I'll understand the material. And that's exactly what happened in previous lessons - when I got visual explanations, I was able to understand the concepts just fine. So, it's likely that if I get visual explanations now, I'll be able to understand the material again.

So, the true explanation has to be Hypothesis 1.

Wouldn’t it have been easier to just make a T-chart of invalid and valid formulas?

e.g.,

Invalid | Valid

S,S,S | M,M,S

A,M,S | M,A,S

A,S,S (lol) | S,A,S