This was an amazing lecture I'd watch more of her lectures if there are anymore due to her ability to explain things so clearly.

4/5 timed & 5/5 blind review!!!

I grasp the concept more with video lectures I'm not sure why this isn't the case for this giant section.

we finally made it to this section!!!

• Here, we examine another formal argument pattern: if “most A are B” and “most A are C,” then we can conclude that “some B are C.” Last formal argument needed to be familiar with. Formal argument #6. This is called “two split most". This has to do with the generic form of the argument where it has to do with the generic form of the argument. Has to do with the shape of the argument. This is an argument where you get two premises that say [A most B]. So most [As are Bs]. Another premise that says [A most C.]  So most [As are Cs.] When you have two premises that look like that, what must be true is that [some Bs are Cs.] There has to be a B and C intersection. 

• Premise: A - m → B       - m → C

• Conclusion: B ← s → C 

  • A B, A B, A B C, A C, A C 

• Example #1: “Most almonds grown in California are produced for domestic consumption. Most almonds grown in California require intense irrigation. Therefore, some almonds produced for domestic consumption require intense irrigation.” 

  • The conclusion follows logically! 

  • If it’s true that most almonds are produced for domestic consumption, and it simultaneously is true that most almonds also require intense irrigation, well, there’s at least one intersecting  almond that requires both intense irrigation and is produced for domestic consumption. 

    • Premise/Chain Link: [Almonds - m → Domestic]         [ - m → Irrigation]

  • Conclusion: [Domestic ← S → Irrigation] 

• RECAP: 

  • Formal argument #6 “two split mosts”: Most As are Bs. Most As are Cs. Therefore, some Bs are Cs. 

  • All arguments that instantiate this form are valid. We can substitute any concept for A, B, and C and the argument will still be valid. 

  • Premise: [A - m → B]

        [ - m → C]

  • Conclusion: B ← S → C 

• “Some cafes in the city serve hand poured single origin coffee.” 

  • “Some” quantifies over the subject set “cafes in the city.” It pushes “some” members in that set over to the predicate set “serve hand poured single origin coffee.” city ← S → hpsoc hpsoc ← S → city The “some” arrow is reversibly read. (A ← S → B) ← → (B ← S → A) That means if it’s true that some cafes in the city serve hpso coffee, then it’s true that some cafes that serve hpso coffee are in the city.

• “Most gold mines that supply unprocessed ore to Casterly Rock are running low on gold deposits.” 

  • “Most” quantifies over the subject set “gold mines that supply unprocessed ore to Casterly Rock.” It pushes “most” members in that set over to the predicate set “are running low on gold deposits.” Gold Mines Supply CR -- m → Low on Gold Deposit “most” are not reversible!

• “Many turtles swim across the Pacific to return to their hatching beach.” 

  • “Many” quantifies over the subject set “turtles.” It pushes “many” members in that set over to the predicate set “swim across the Pacific to return to their hatching beach.” 

  • If you want, you could translate “many” to “some.” I just want to make sure that you don’t mistakenly think that “many” turtles swim across…means that “most” turtles swim across because that's not true. 

• “Prof. Sprout’s Mandrake inspections are usually conducted on Mondays.” 

  • The quantifier here is “usually.” We’re talking instances of Prof. Sprout inspecting her Mandrakes. “Usually” says that “most” of those instances are “Mondays.” Mandrake Inspection - - m → Monday Does this mean that on most Mondays, Prof. Sprout inspects her Mandrakes? No. Absolutely not. For all we know, she only inspects her Mandrakes ten times a year. Eight of those ten inspections are on Mondays. There are more than fifty Mondays in any given year. Be careful not to read ( A - - m → B) as ( B - - m → A)

• “Fewer than half of the kittens adopted yesterday went to homes with children” 

  • “Fewer than half” means “most not.” Fewer than half of the apples are rotten means that more than half of the apples are not rotten. The quantification is over the subject set - “kittens adopted yesterday” - and the “not” gets pushed onto the predicate set - “[not] went to home with children.” [ Kitten - - m → /Home -children ] 

• Here, we take a step back and get some perspective on why we care about quantifiers. 

• “Many large pharmaceutical companies are racing to develop the vaccine for a novel coronavirus. This makes sense economically and morally as there are billions of dollars to be made and millions of lives to be saved.” 

  • If the statement above is true, then which one of the following is most strongly supported?

  • (A) Most large pharmaceutical companies are racing to develop a vaccine for a novel coronavirus. (this is wrong don’t confuse most for many!!!!!) it does not imply most! Not true!!!

  • (B) Some pharmaceutical companies are working on a vaccine for a novel coronavirus. (correct answer choice)  

  • (C) Some pharmaceutical companies are investing all their resources on developing a vaccine for a novel coronavirus. (wrong) It does not mention in the passage “investing all their resources” this is never mentioned and not supported. Just because companies are racing to develop a vaccine doesn’t imply that they are investing all of their resources. 

• RECAP: 

  • Much of the LSAT is about making supportable inferences. It’s important both to recognize when an inference ought to be made (e.g., “many” implies “some”) and to recognize when an inference is unsupported (e.g., “racing to develop” doesn’t imply “investing all resources”). 

• Here, we directly compare the meaning of “some,” “most,” and “all” in order to see how some quantifiers can imply others. “All” is a stronger claim than “Most.” 

  • All dogs like bacon → Most dogs like bacon   dog → bacon dog - m → bacon

• Let’s look at the relationship between “most” and “some.” “Most” is a stronger word than some and therefore a much stronger claim. What can be inferred from “most” is “some.” 

  • Most cats are funny → Some cats are furry. [The word “most” implies “some”]               cat - m → furry cat ← s → furry 

• So now we know “all” implies “most” and “most” implies “some.” That additionally means that “all” also implies “some”. This is because “all” implies “most,” and “most” implies “some.” So, therefore, “all” must also imply “some,” which means if we know that “all dogs like bacon,” it must also be true that “some dogs like bacon.” [dog ← S → bacon]. If the “all” claim is strong enough to support a “most” claim, it must also be strong enough to support an even weaker “some” claim. 

• RECAP: 

  • “All” implies “most,” which implies “some.” 

  • If “all X are Y," then “most X are Y” and “some X are Y.” 

  • Id “most A are B,” then “some A are B.” 

Here's my clean version notes with step-by-step breakdown on the first example.

• In this lesson, we start our language of Lawgic when dealing with relationships involving the quantity “most”. We first have to learn the element in Lawgic that represents “most,” and it’s this “most” arrow [ -m→ ] Notice how the “most” arrow is unidirectional. It is a one-way street, just like your standard conditional arrow. It does not point in both directions. That’s different from the “some” arrow, which is a bi-directional arrow meaning it points in both directions.  You must read “most” in an unidirectional way. You cannot read it reversibly. 

• Example #1 Lawgic: “Most students in Mrs. Stoops’s class can read.” 

  • Step 1: This is a claim in English that is amenable to translation into Lawgic. And to do that, we identify the indicator or quantifier. “The word “most.” 

  • Step 2: We identify the two main concepts or sets. (first set) the set of students in Mrs. Stoops’s class. (second set) is the set of students or people who can read. 

  • Step 3: Assign Symbols: (students) (read) 

  • Step 4: Add the “most” arrow. The Lawgic says (students) -m→ (read). Need to emphasize that the arrow is unidirectional. This is the point of difference between the “most” arrow and the “some” arrow. You cannot read this the other way around. 

• RECAP: 

  • To translate “most” claims to Lawgic, use the unidirectional “most” arrow: (-m→). The arrow is unidirectional because the “most” intersection relationship does not work both ways: “most A are B” is not identical to “most B are A.” 

Step by step breakdown:

• In this lesson, we start using our language of Lawgic when dealing with relationships involving the quantity “some”. “Some” must include at least “one” or could include up to “all”. 

• In Lawgic, the quantifier “some” is represented with this bi-direction arrow ( ←S→ ) with an S in the middle of it. The “S” in this arrow is to distinguish it from the bi-conditional arrow ( ← → ). 

• The quantifier some ( ← S → ) which expresses an intersection. Let’s look at an example…..

  • “Some students in Mrs. Stoops’s class can read.” 

  • Step 1: Identify that this is a statement, this is a claim that is amenable to translation. The way to do that is to (first) identify/notice the quantifier. Or the intersection indicator. In this instance it’s the word “Some”. 

  • Step 2: Identify the two concepts. Typically, they are sets. The [first concept] is “students in Mrs. Stoops’'s class” & the [second concept] is “student or people can read”. 

  • Step 3: Assign Symbols to represent these two sets. (Student) to represent students in Mrs. Stoops’s class & (Read) to represent the student/people who can read. 

  • Translation Into Lawgic : Add the “Some” arrow! (student) ← S → (read) This means you can read this arrow either from left to right or from right to left. What that means is that this statement here, “student ← S → read,” is identical to the statement “read ← S → student.” In Lawgic, these two claims are the same. 

  • Translating Back Into English: What it means is that “Some students in Mrs. Stoops’s class can read” is identical in meaning to “Some student that can read are in Mrs. Stoops’s class.” 

  • Example→ “Some cats are pets” is identical to the claim that “Some pets are cats.”  Translate into Lawgic: (c ← S → p)  (p ← S → c) All four of these expressions are getting at the exact same idea, which, again, is just the idea of an intersection between two sets. 

• RECAP: 

  • To translate “some” claims to Lawgic, use the bi-directional “some” arrow (← S →). The arrow is bi-directional because the intersection relationship works both ways: “some A are B” is identical to “some B are A.” 

Clean version of my notes...

• Here, we look at the range of quantifiers that the word “some” can describe. In the previous lesson, we established that the quantifier “some” has a lower boundary. It’s ambiguous, but that doesn’t mean all interpretations are reasonable. There are boundaries that carve out reasonable interpretations. 

• “Some” must include at least “one”. → In other words, if the claim that some students in Mrs. Stoops’s class can read is true, then what must be true is that at least one student in her can read. That’s what we mean by the lower boundary. 

  • “Some students in Mrs. Stoops’s class can read” 

  • At least one student can read ← must be true. 

  • “Must be true is a lower bound” It’s saying that below this boundary, the claim has to be false. The false phrase would be “no student can read”. That statement is incompatible with this statement that some students in Mrs. Stoops can read. 

• In other words, inclusive of one and exclusive of zero. That must be true. Could all 20 students be listed as the ones who can read yes because it doesn't have to be true but it could be true. All 20 students in her class being able to read is not being excluded by the claim that some students in Mrs. Stoop’s class can read. 

• Think about the quantifiers “some” as a range. The range of “some” starts with the lower boundary of at least one, but it could go up to include as many as “all”. 

• RECAP: 

  • The lower boundary for “some” is “at least one”. “Some” does not have an upper boundary. It could potentially include all members of the group in question. 

  • Think of “some” as establishing a range that starts with a minimum of one (the lower boundary) and could extend to include the entire set. 

I got the blind review correct but the initial attempt I didn't get correct I feel like I try and find the one that feels right initially instead of looking for the one pulled/supported from the passage.

clean version of my notes;

• Here, we tackle a special category of conditional relationships: those in which two conditions are both sufficient and necessary for each other. What are Bi-Conditional Claims: They are just the conjunction of a uni-conditional claim and its converse. 

• Bi-Conditional Claims: 

  • Luke will become a Jedi if Yoda trains him and Luke will become a Jedi only if Yoda trains him 

  • Yoda’s training is sufficient and necessary for Luke becoming a Jedi.

  • Translating into Lawgic: (yoda - t → luke- j) (luke-j → yoda - t)  [&]

  • Bi-Conditional in Lawgic: (yoda-t) ← (luke-j)  it then looks like this (yoda-t ←→ luke-j) 

  • So what does the bi-conditional mean? It means that Yoda’s training is sufficient and necessary for Luke becoming a Jedi. 

  • The contrapositive of this will look like this: (/yoda-t ← → /luke - j) 

• Indicators for Bi-Condirionals: 

  • If and only if 

  • If but only of 

  • Then and only then 

  • Or…but not both 

  • If…then…but not otherwise 

• Examples for Bi-Conditionals: 

  • Luke will become a Jedi if and only if Yoda trains him 

  • Luke will become a Jedi if but only if Yoda trains him

  • Luke will become a Jedi if Yoda trains him but not otherwise. 

  • [These are all sufficient and necessary conditionals] 

• RECAP: 

  • Uni-conditionals express sufficiency (Yoda’s training is sufficient for Luke to become a Jedi) or necessity (Yoda’s training is necessary for Luke to become a Jedi). 

  • A bi-conditional indicates that the two conditions are both sufficient and necessary for each other (Yoda’s training is both sufficient and necessary for Luke to become a Jedi). They are mutually dependent. One occurs if and only if the other occurs. 

  • Bi-conditionals claims are represented in Lawgic with the bi-conditional arrow: ← → 

• Q1: “Unless we drive out the poachers, none of the pandas that relocated to this part of the forest will prosper.” 

  • /drive out poachers → (relocated panda → /prosper) 

  • /drive out poachers and relocate panda → /prosper 

  • We’ll start by treating the clause following “unless” as the exception. The other clause will be the rule. Rule: “none of the pandas that relocated to this part of the forest will prosper.” Exception: “we drove out the poachers” Lawgic Rule: (relocated panda → /prosper) Lawgic Exception: (drive out poachers) 

• Q2: “No restrictions should be placed on the sale of merchandise unless the scale of that merchandise could endanger innocent people.” 

  • Rule: No restrictions should be placed on the scale of merchandise. 

  • Exception: Sale of that merchandise could endanger innocent people. Lawgic Rule: (sale-merch → /restrict) Lawgic Exception: (merch -could endanger-inno) 

• Q3: “Opera companies have to produce the most popular operas, unless they receive funding from the National Endowment for the Arts.” 

  • Rule: Opera companies have to produce the most popular opera.

  • Exception: They receive funding from the National Endowment for the Arts. Lawgic Rule: Opera -company → prod-most-pop-operas

Lawgic Exception: fund-NEA

Domain: Opera-company /fund-NEA → prod-most-pop-operas.

• Q4: “A pet adoption center with at least ten years of continuous operations will be supported by the Mittens Foundation if it shelters more than fifty animals.” 

  • Domain: Pet adoption Center 

  • Rule as embedded conditional: shelter 50+ → (10years →supp-MF) 

  • Rule with sufficient conjuncts: shelter 50+ and 10 years → supp MF

  • Lawgic Rule: 10 YRS → Supp MF

  • Lawgic Exception: /Shelter 50+ 

• Q5: “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.” 

  • Domain: Knowledge of the existence of a particular fact is an element of an offense. 

  • Rule: If a person is aware of a high probability of its existence, then such knowledge is established. 

  • Exception: He actually believed that it did not exist. 

I have notes:

• Example 1: “An engaging plot will guarantee a novel’s commercial success.” 

  • “Engaging plot” (sufficient condition) & “novel’s commercial success” (necessary condition) → we know this because of the phrase [will guarantee]. 

Plot → Success 

• Example 2: “Mastering conditional logic requires some amount of memorizing conditional indicators.” 

  • “Mastering conditional logic” (sufficient indicator) & “some amount of memorizing conditional indicators” (necessary condition) → we know this because of the phrase [requires]. 

Mastery → Memorization 

• Example 3: ‘The students who mastered logic saw improvements in their PrepTest scores.” 

  • “Students who mastered logic” (sufficient indicator) & “improvements in their PrepTest scores” (necessary condition)

    subject → predicate 

Mastery → Improve 

• Example 4: “The kingdoms in Westeros whose economies rely predominantly on trade support foreign policies that aim to secure peace.” 

  • “Kingdoms in Westeros whose economies rely predominantly on trade” (subject/sufficient condition) & “foreign policies that aim to secure peace.” (predicate/ necessary condition) 

Subject → Predicate 

Trade → Peace 

I got it right on the blind review, but I think it's because I focused more on the order and structure of the passage rather than just looking first at the answer choices. Fully understanding what you are reading first in order help's you figure out an answer choice that's 100% correct/provable.

I study by memorizing the steps here is my work if it helps others with the same study style as mine:

• Question 1: “Lazy cats never develop heart disease”

  • Step 1: Find Indicator: “never”

  • Step 2: Identify Ideas: lazy cats vs. never developed heart disease. 

  • Step 3: Apply symbols to these ideas: (LC) → (/HD)

  • Step 4: Apply the Translation Rule: (LC) → (/HD)

NEGATE (HD) → (/LC) 

• Question 2: “No holiday falls within the month of August”

  • Step 1: Find Indicator: “NO” from group 4 indicator words. 

  • Step 2: Identify the Ideas:  Holiday vs. Within the month of August. 

  • Step 3: Apply Symbols to the ideas: (H) Holiday vs. (Within August). 

  • Step 4: Apply the translation rule: (H) → (/within August) 

  • NEGATE: (within August) → (/H) 

• Question 3: “No birds are trees.” 

  • Step 1: Identify the indicator word and what group it’s in: “no” from group 4. 

  • Step 2: Identify the ideas: Birds vs. Trees

  • Step 3: Apply symbols to these ideas: (B) vs. (T)

  • Step 4: Apply the translation rule: (Bird) → (/Tree)

  • NEGATE: (Tree) → (/Bird) 

• Question 4: “Mesopotamian cities never had marketplaces.” 

  • Step 1: “Never” Group 4

  • Step 2: Mesopotamia cities vs. Marketplace 

  • Step 3: (MC) vs. (MP) 

  • Step 4: (MC) → (/MP)

  • NEGATE: (MP) → (/MC) 

• Question 5: “None of the recent technological advances in producing electric power at photovoltaic plants can be applied to producing power at traditional plants” 

  • 1. “None” Group 4

  • 2. Recent Technological advancements at Photovoltaic vs. Cannot be applied to traditional plants. 

  • 3. (RTAP) VS. (/ATP) 

  • 4. (RTAP) → (/ATP) 

  • NEGATE: (ATP) → (/RTAP) 

GOOD LUCK !!!!

• Here we discuss the GROUP 4 indicators, which involve negative one of the ideas before making it the necessary condition. Group 4 indicators are: → 

  • NO 

  • NONE

  • NOT BOTH 

  • CANNOT

• Translation Rule: “pick either idea, negate that idea, then make that idea the necessary condition. The other idea from GROUP 3 falls into the place of a sufficient condition.”

• EXAMPLE #1: “None of the Americans attended the dictator’s party.”  

  • Step 1 Identify the Initial Indicator: → here is the word “none” that's group 4. 

  • Step 2 Identify the two main concepts: → main concept (subject) none of the Americans other concept (predicate) attended the dictator’s party. 

  • Step 3 Assign symbols to the two main concepts: → American (A) and use (ADP) for attending the dictator’s party.

  • Step 4 Apply the translation rule: (ADP) → (/A)

1. → (/ADP)

Translating this new form back into English: “If one is an American, then one did not attend the dictator’s party.” and the other translation looks like this → “If one attended the dictator’s party, then one is not an American.” 

• Question 1: “Without physical exercise, health deteriorates.” 

  • Identify the logical indicator → “without” which is part of group 3. 

  • Next Identify the idea: → one idea is physical exercise, and the other idea is health deterioration. 

  • Let's follow through with group 3 translations by labeling these ideas.         (PC )  (HD) 

  • Let’s negate it →     /(PE) → (HD)   or /(HD) → (PE) 

  • Translating back into english: → “if there's no physical exercise, then my health is going to deteriorate.” “If my health is not deteriorating, maybe lots of other things are, but for sure I’m getting physical exercise.”

• Example #1: “Blackouts will occur unless the heat waves abates.”

  • Translation Step 1: Identify the conditional indicator: The word “unless” is our identifiable conditional indicator. 

  • Step 2: Identify the two main concepts (or groups, categories, events, or ideas): Blackouts will occur(first concept) and the other unless the heat waves abate (second concept).

  • Step 3: Assign Symbols to the main concepts: /BO → HWA → IF THE HEAT WAVE DOESN'T ABATE --> BLACK OUT OCCURS.

  • Step 4: Apply the translation rule LAWGIC: /BO → HWA

  • CONTRAPOSITIVE: /(HWA) → BO

  • Translating back to english: “If the heat wave doesn’t abate, then blackouts will occur.”

• “Which can be used as a referential word in various contexts. It can refer either to a noun with all of its modifications, or it can refer to an entire clause that is subject and predicate. 

• Referring to a noun: “Azedcorp, which owns a majority stake, has steadfastly refused to sell. 

  • The word “WHICH” in this sentence refers to a Azedcorp. → You can swap out the referential “which” for its referent. 

  •  In doing so, you expand this sentence into two sentences. #1: Azedcorp currently owns a majority stake. #2: Azedcorp has steadfastly refused to sell. The second usage is where “which” refers to an entire clause which you typically find at the end of the sentence. 

• Referring to a clause (subject and predicate:) “A pet makes one’s time at a retirement home more rewarding, which can be important to more people as the average life span of our population increases.”

  • What is the subject? The pet is the subject. 

  • What is the predicate? Makes one’s time at a retirement home more rewarding. 

  • The second clause begins after the comma with the word “which.” 

• We could split this sentence into two sentences by adding a period and swapping out the word “which” for “that”. #1 Sentence: A pet makes one’s time at the retirement home more rewarding. #2 Sentence: (Swap “which” for “that”) That will be important to more people as the average life span of our population increases. 

  • Recap: “Which” is often used as a referential. It can refer to a noun or an entire clause. 

• Referential: are words or phrases that stand in for something stated elsewhere in the text (usually earlier). 

• Example #1:“Botanists at the Ben Gurion University recently discovered plants that can extract phosphorus from the sand covering its leaves.” “They are conducting experiments to better understand the mechanism which enables such extraction.” 

  • →“They” is a referential word, and in most cases, it’s simply standing in place for something else that appeared earlier in the text. 

  • → In the second sentence, “such extractions” is a referential phrase. This is because it’s a pointer, it’s just standing in for something already previously stated. 

  • →“It’s” is also a referential it’s derived from the previous word it’s referring to which are plants. 

  • The “referencial” is the pointer, the “referent” is the target, it’s the thing that’s being pointed to. 

• Example #2:“Some religious leaders who undertake reforms do so out of an intrinsic commitment to philosophical ideals.” 

  • → “do so” is the referential word in this sentence. If you want to understand what “do so” means, you have to look back at the earlier part of the text. They are pointing to "undertake reform”. 

• Example #3:“A turning point in the transition to democracy came when privileged people in society who had been part of its support base realized that the authoritarian regime is dispensable.”

  • → “It’s support base” is a referential. It points to the authoritarian regime. 

  • Who’s support base? The authoritarian regime is the support base. In this rare case the referential is forward in the text not back. 

• Example #4:“African American folk tradition does not sharply differentiate reality into irreconcilable dichotomies between good and evil. This is consistent with the apparently dual aspects of the blues and spirituals.”

  • → “This is” is a referential word. → it points to the entire sentence preceding it. It consists of a parent duality. 

• Recap:

  • Referential are words or phrases that reveal their meaning by pointing to another set of words (which we call the referent). They often point backwards but they can point forward as well. They can point to things or to actions. They can also point to entire sentences or paragraphs. Cultivate a habit of explicitly identifying referential and linking them back to their referents. Otherwise, you will get lost in the text. 

yes ! same here