1-3 LR questions in the test may directly talk about an experiment. And the answer is that they didn't randomize/control for all variables/etc.

Using the example

Most of almonds are grown in California: Okay, let's say 80% of almonds produced in the US are grown in California. 100 tons of almonds. Whatever.

Now, most of produce grown in California is exported to Brazil: Again, let's say 80% of produce goes to Brazil. Maybe California sends a lot of avocados, and a lot of strawberries, etc.

Some almonds are exported to Brazil:....wait what? That COULD BE true and it also COULD NOT be true. Notice that the 80% of California's produce COULD OR COULD NOT include almonds. They could be watermelons, avocados, strawberries, etc. We honestly don't know! For all we know, all the almonds grown in California could be exported to NY.

See how different that is from this:

Most of almonds produced are grown in california. Most of almonds produced are exported to brazil. Therefore, some almonds grown in california are exported to Brazil.

Do you see how much tighter that argument is?? We know FOR A FACT that most of the almonds are being exported to brazil. The other prompt just said "most produce." In conclusion we can assume there is some overlap.

"However, if you have a bucket of A then a bucket of B, and scoop from the B bucket into C, none of A will make it into C. "

I think this is slightly inaccurate.

You pour a bucket of A into bucket B. (All Philharmonic know how to play violin)

You take a scoop from bucket B into C (Most that know how to play violin don't play well).

You take a look at bucket C and you CANNOT make a conclusion. Did the scoop we took include A? Who knows??? In the example, we don't know if the scoop from C includes A. In reality, it probably does not include any members of the philharmonic.

Writing one more example for good measure.

All Jets fans live in New York. Most of the people in New York like to go for runs. Therefore, some Jets fans go for runs.

Can we make a conclusion on our Bucket C (people that like to go for runs)? No! We cannot say with certainty that these include Jets fans. They could include anyone in New York who is a giants fan, or doesn't watch football, or likes opera, or [insert random detail] etc. In fact, in my experience, as a Jets fan, most Jets fans are out of shape and probably don't run (no offense to Jets nation).

Another one for good measure:

All lawyers have taken the LSAT. Jamie has taken the LSAT. Therefore, Jamie is a lawyer.

In lawgic: Lawyer-> LSAT

J LSAT

????

We can't draw a conclusion. Jamie could be a doctor, a mechanic, etc.

I read through the comments and to answer it quickly:

"Only birds migrate south in winter. Then B would be the necessary condition in Lawgic" is a different argument.

You are correct. That's the point J is trying to make.

The unless rule is almost more crucial here: negate sufficient and make the clause after "unless" the necessary condition.

/no student is sorted into Gryffindor-> exhibit bravery

the double negative cancels out

students are sorted into gryffindor -> exhibit bravery

Another way to see this relationship is realize that there is at least one food, the almond, that is produced for domestic consumption and requires irrigation.

Applying that to any argument

Most jets fans are in NY. Most jets fans like hot dogs. Some people in New York like hot dogs.

We KNOW there are jets fans in New York and we also know that Jet's fans like hot dogs. They very well could be the people in in New York that like hot dogs, referenced in my conclusion. Therefore there are at least some people in NY that like hot dogs.

questions 6-8 don't relate to the previous lessons and might work better in a separate unit on "negating claims" in general#feedback

+1 student who can read ←s→ Ms. Stoop's class

I don't believe "some implies not all"

in natural english, we would just say "all students can read." But, if we ignore that part of our brain that wants to say "all," and focus on the logic, this lesson is correct.

Some could = 1,2,3.....20

Person 1: Some students in the class read

Person 2: How many?

Person 1: 20

Person 2: Great, you are correct in stating that some students in the class read.

So don't think of it as "some implies not all"... think of it as "some implies some"

Yes, and more conceptually, "only if" is another way of saying "membership in subset X means membership in superset Y."

membership in becoming a jedi means membership in superset of being trained by Yoda.

Plain english...it's the only way!

I was scrolling through explanations and this sums it up perfectly from

kimyongjoon0907: Every action which should be provided by someone could result from other than specific organization, then the meaning changes.

Let's assume "ppph->provided"

Let's make a big circle for "things necessary for human life should be provided"

provided (_)

if you put "organizations whose primary purpose is promotion of human health" or "Org for health" inside it, you get

provided (org for health() )

There's a HUGE problem with this. Now we are saying that OTHER ORGANIZATIONS can exist in this circle of providing. For example, organizations whose primary purpose is equity. Organizations whose primary purpose is racial justice. All these groups now have to provide.

That is a far departure from the original sentence. The original sentence is almost saying "Only organizations should provide whose primary purpose is human health."

So the rule you made"pph--> provide" is inaccurate. What better translates onto it is

"provide--> ppph." then we capture the meaning of the sentence ....

that of all the actions that an organization whose primary purpose is human health,

one of the actions should be provide....

ppph((provide_))

OR ppph (educateheal_provide)

I didn't see it at first but we are pretty much blinding ourselves to one sufficient condition (in this case, living in NY)

By doing that we can take away some of our notation, which will speed things up in the LR section.

For example"

All football players on Alabama that have played for more than a year will have an NIL deal if they score more than 2 touchdowns.

If the LR question was going to tease out something about scoring touchdowns, we can just cut the bit about Alabama players.

if played for more than a year + scored 2 touchdowns -> NIL deal

then we can infer that

/NIL deal-> /playing for a year or /scoring 2 touchdowns

BUT it's still important to remember we are ONLY talking about Alabama players

both situations should be met for the necessary condition.

X->Y AND Z

Only one, the other, or both (negative) situations should be met to trigger the sufficient condition.

/Y or /Z-> /X

I agree. I feel like #5 shows the benefit of breaking down a disjunction. It shows you the two events that would need to happen (or not happen).

For example, we need to consider that the person must NOT be 21 and ALSO must not be 21+

Yeah that works too, it's all semantics

X is A

vs.

X is a member of the set of A

Negating the conjunction is more intuitive:

If M-> N and O

Forgetting everything we learned here - we NEED N and O to have M

Remembering logic rules - to be in the subset of M we need to be in the superset of N and O

My interpretation - if you're in the tiny world/circle of M you need to be in the larger world/circle of N and O

What does this tell us, intuitively? If for some reason we don't have N, then we're screwed. We won't have M. If for some reason we don't have O, then we're screwed too, and we don't have M.

In either case: /N OR /O->/M

Either of those events happening, or just one, will trigger /M.

Looking at disjunction:

/N or /O->/M

Okay sweet, if we don't have either event, the /M will trigger. What if we want to get to M? What logical inference can we make?

We normally can't just say "M" (because this goes against everything we're taught on switching sufficient and necessary) but in this case we can take the contrapositive.

So M -> / (/N or /O)

Then to have M, means we MUST have NOT (/N) or (/O). Putting it in english, we must have both not N being not adopted or not O being not adopted...

we must have both N being adopted or O being adopted...

I don't know how to articulate the jump from "or" to "and" but, clearly, FROM OUR UNDERSTANDING OF THE SCENARIO, we need BOTH these kids adopted.

Again, if N's not adopted, that screws us up. And if M's not adopted, that screws us up too.

Full transparency, "/or = and" is confusing for me from a logical point of view...but when I think of the scenario it makes sense.

CS → AF or JF

is fundamentally different in meaning from

CS-> AF

or

→JF

In the first case, if the chancellor succeeds, we know FOR A FACT that one event will be triggered, the other event will triggered, or both can be triggered. The two events are thus RELATED to each other.

In the second case, we are setting ourselves up for failure. We are treating the two events as separate from each other when they are not; they are related to each other. We NEED one OR the other.

This is very different frame of mind when thinking of disjunction in sufficient conditions, where one event can trigger the other NO MATTER WHAT HAPPENED WITH THE OTHER EVENT.

It's hard to see now but when we have to answer "must be trues" this will make more sense.

The quickest way to understand, for me, was to remember that we can only draw logical conclusions from the sentence in front of us.

The sentence says NOTHING about what happens if /M.

BUT we do know what happens if /N or /O...those are definitely triggers for another event (/M)

Isolating N from O also allows us to see that two separate events are triggered to happen.

For example, if you win a million dollars you will buy a house and quit your job.

They are two separate events that are triggered and, as Sidhant says, we can't draw relationships between them.

This will just help us down the road.

I think you are mistaking X "having" A for X "being" A/ X "being a subset" of A.

X is A...and A->B...therefore X--> B

"If" is an indicator for a sufficient condition (If...then...) structure. Another way to think of it is "if" is the trigger for the necessary condition or outcome.

If this speech happens, then Palpatine will not get emergency powers.

totally agree, this is ridiculous #feedback

For something as foundational and challenging as conditional logic, you'd think there would be AT LEAST ONE video explanation for each exercise. Then you could use that video as a basis to learn the other examples.

"None of the flowers in the garden bloom in the winter"

I agree it is a totally different meaning semantically, but logically it's the same situation. It depends on where you make the cut

"None of the flowers in the garden bloom/ in the winter"

"None of the flowers in the garden/ bloom in the winter"

Let's say the prompt was asking us about the winter time, we can switch gears and analyze if winter time precludes flowers in the garden blooming. Alternatively, if we want to figure out if blooming in the winter precludes being a flower in the garden, we can analyze that too.

It's not so much about "cause"... I think cause implies causation. But the "ingredients" part, I totally agree with.

"Only if x, then y"

I first break it down into the typical conditional format: "if y, then x"

The visual representations help me a lot and help me see that:

X ( Y( ))

Secondly, I tell myself that, in the larger world of X, the smaller world of y DEFINITELY exists.

That sounds way more intuitive to me. In a world of countless possibilities, there is a world "X" that has a smaller world "Y" that exists in it.

And to get to, or to travel to "Y", you have to first travel to X.

THEREFORE, only if X, then Y.

hope this helps!