Howdy, Stranger!
It looks like you're new here. If you want to get involved, click one of these buttons!
Categories
- 33.4K All Categories
- 28.1K LSAT
- 17.1K General
- 5.2K Logical Reasoning
- 1.4K Reading Comprehension
- 1.7K Logic Games
- 70 Podcasts
- 191 Webinars
- 10 Scholarships
- 194 Test Center Reviews
- 2.2K Study Groups
- 111 Study Guides/Cheat Sheets
- 2.5K Specific LSAT Dates
- 31 November 2024 LSAT
- 18 October 2024 LSAT
- 9 September 2024 LSAT
- 38 August 2024 LSAT
- 28 June 2024 LSAT
- 4 April 2024 LSAT
- 11 February 2024 LSAT
- 22 January 2024 LSAT
- 38 November 2023 LSAT
- 43 October 2023 LSAT
- 14 September 2023 LSAT
- 38 August 2023 LSAT
- 27 June 2023 LSAT
- 30 Sage Advice
- 5K Not LSAT
- 4K Law School Admissions
- 13 Law School Explained
- 10 Forum Rules
- 636 Technical Problems
- 286 Off-topic
Related Discussions
12 Likes
LR Study Guides Thread
emli1000
Alum Member Inactive ⭐
I was wondering if we could upload our study guides in this post for those taking the June and upcoming LSATs can always come back to this.
Comments
CAUSATION Lesson 1 of 20
Universal quantifiers: sufficient/necessity relationship
Existential quantifiers: intersection relationship
Causation: causal relationship
ALL THREE IDEAS ARE RELATIONSHIPS
CAUSATION THEORY Lesson 2 of 20
Causation theory:
1. Implies- Correlation- A causes B: implies that there is correlation, if a does NOT cause b, then no causation. Contrapositive- if there is no correlation then there is no event of causation.
2. Implies- Chronology- a causes b; it has to be the case that a precedes b. A→B
3. Strongly Suggests- No Competing Cause- if this doesn’t exist; it’s just that it is less likely a cause now. This strongly suggests that A→B and that C did NOT cause A and B. C isn’t necessary to establish that A causes B, but if it exists and its clear that it doesn’t cause B then it helps establish causation between A and
CORRELATION Lesson 3 of 20
Definition: Empirically Observed Co-Variance
Few Instance: Co-Incidence:
-Two phenomenon happen together.
Gives Rise To: Four Possibilities
Remember: Does NOT Imply Causation
-Correlation -> Causation
Causation -> Correlation
- Correlation implies co-incidence ... but not the every other way.
-Co-incidence: just that one instant. Does NOT cause correlation
-Remember correlation does NOT imply causation
CORRELATION IDEAS Lesson 4 of 20
-Definition: Emprirically Observed: Out in the world-it’s data
Co-Variance: Change that happens together
-EX: Fire & Firefighters-correlated
The size of the fire and the numbers of firefighter
Firefighters do not cause fire- therefore it’s not causation
The size of fire is correlated with numbers of firefighters =/= firefighters cause fire
**The bigger the fire, the larger the number of firefighters (Correlates)
Therefore, firefighters make the fire more severe->erroneous argument. Correlation does not imply causation.
FOUR POSSIBLE EXPLANATIONS (which Correlation gives rise to provided A Correlates with
1. A caused B
Ex. Fire cause firefighters to be present
2. B caused A
Ex. Firefighters set fire to buildings
3. C caused both A & B
Ex. (A) Ice cream sales correlated with (B) drowning – (C) Summer is the true factor
4. No Relationship
Ex. As British colonies gained independence, electricity became more widely available in the world. Both factors, which are empirically observed just, happened at the same time and they are not in causal relationship.
*Alternative Cause-A & B, it’s not that A caused B or B caused A; it’s something else that caused A by itself & something else that caused B by itself.
CHRONOLOGY Lesson 6 of 20
-Remember: Chronology does NOT imply Causation
EX: Sun dance correlates with Sunrise-perfect correlation but
• Chronology & Correlation together does NOT imply Causation!
• 4. No relationship explains this
CAUSATION STRATEGY Lesson 7 of 20
1st thing to distinguish when Causation is in LR
It’s Always in Error: If Causation is in the Conclusion or it has assumed its causation (almost always in error) be in alert because something has gone wrong
2nd thing to distinguish
Whether they gave you a correlation that let them conclude the causation or a Co-Incidence causation in the Premise
Correlation: Repeated observed co-variance
EX: The runners that stretch their legs before running tend to get hurt more often.
A lot of data points—the runner/people who run/people who stretch before they run/people who do not stretch before they run THEREFORE you get different results from that and that is correlation.
Co-Incidence: just that one instant. Does NOT cause correlation
EX: Tom went running that day and he didn’t stretch and he hurt his ankle.
When you’re given a Co-Incidence what you want to check for is Competing Explanation: the introduction or denial of a competing explanation or hypothesis
Stimulus: Premise gives us either correlation or co-incidence
Argument proceeds to assume causation or concludes causation
*Correlation check (3)
(1) Chronology- Check to see if the order is reversal: Causes must precede effects
(2) Third common Cause- Introduce or Blocked- perhaps the “cause” and the “effect” are both effects of a common “third” cause
(3) Data Set- Competing or corroborating sets- competing data or corroborating data
**Correlation means 2 or more things happen at the same time over and over (repeatedly) while co-incidence means 2 things happen at the same time but not repeatedly, probably one or two times. Neither correlation nor co-incidence means causation.
3 WAYS TO IDENTIFY PREMISE AND CONCLUSION Lesson 8 of 16
-INDICATORS: words that indicate P & C
PREMISE: Given that, Seeing that, For the reason that, In as much as, Owing to, As indicated by, After all, On the grounds that
CONCLUSION: Consequently, therefore, As a result, So, Clearly, It follows that, Accordingly, We may conclude, Entails that, Hence, Thus, We may infer that, It must be that, Implies that, That is why
Words or phrases that are usually followed by premise(s) but contain the conclusion: For, Since, Because
-WHY?!: why should I believe that sentence? And refer to the other sentences for support? Then that sentence is the conclusion.
Involves trial and error. Take the sentence that you think may be the conclusion (or at random) and ask yourself, “Why should I believe it?” What reasons has the passage provided to accept the supposed conclusion? Try to answer that question by referring to the other sentences in the passage. If those sentences give you a satisfactory answer to why you should believe what the conclusion sentence says, then you may have found the conclusion. Or, you could also be just very easily satisfied.
-PERSUASION: What is the author trying to persuade me that? That is the answer to what a conclusion is. The thing that you are being persuaded of that is the conclusion of the argument.
ADVANACED LABELING Lesson 10 0f 16
-For, since, because
People get confused by these three words, but they are not that confusing. They introduce both premises and conclusions. But, you just have to remember that these three words are locked in to introduce premises and you’ll always find the conclusion in the same sentence. Either it’ll appear before the indicator word, or it’ll appear after the premise.
-Sub-conclusion/major premise
Sometimes arguments get a little complicated and there is more than one conclusion. But only one of them is the main conclusion and the rest are just sub-conclusions, otherwise known as major premises. We’ll see some examples of these.
-Context v. argument
It’s always helpful to figure out what the context or background information is versus what the author’s argument is. Sometimes context is just background information. Sometimes context is actually some other person’s argument. If it is someone else’s argument, you also have to figure out what the premises and conclusions are in the other person’s argument.
- "But", "although", "however"
These words typically indicate a turn away from context - we’re now switching from contextual information, background information - into argument. "Some people say"
This phrase (and its variations) are a common way for Logical Reasoning passages to begin. This phrase always introduces someone else’s argument.-still context
UNIVERSAL QUANTIFIERS Lesson 1 of 40
• Conditional Logic/Universal Quantifiers are very useful for many Logical Reasoning questions and more than half of the Logic Games questions.
• Conditional Logic is a language, just like how English, French, and Chinese are languages.
• Except where as those are natural languages, Conditional Logic is an artificial language used to aid our understanding and manipulation of abstract ideas.
• The major relationship in Conditional Logic is that of the sufficient condition and the necessary condition
ENGLISH IS NOT GOOD ENOUGH Lesson 2 of 40
English
• Numerous ways to express the same idea
• Broader than logic
Conditional Logic/ Universal Quantifiers
• Indicators
• Sufficient & Necessary conditions
WHY LEARN LOGIC
• So this is one of these ideas: “If you're a Jedi, then you use the force.” So in this lesson lets just explore what really this idea is. What does it mean to say, “If you're a Jedi, then you use the force?” Well an idea is just an idea. In order to talk about an idea, in order to give an expression to an idea, we have to impose some kind of language on it. This is already a language.
• So you see this is a different way of expressing that idea. This is a way of expressing the idea in English. This is a way of expressing the idea in venn diagrams. Or in terms of sets, you can think of it like here is a set, here is a members of the set. Here's a larger set which contains the smaller set and here are the members of the larger set. Larger set is called force users, smaller set is called Jedi; really these two are very much overlapping so let's get rid of this and just use this.
• So at bottom, that's the idea you're trying to represent. Every time we talk about this notion of Conditional Logic, every time we talk about this notion of Universal Quantifiers, in short, this entire curriculum, we’re going to be talking about this idea right here. Do you see the sense in which this is a Universal Quantifier? It's quantifying over the entire universe of Jedi, and it’s saying of the Jedi that they’re all force users, not just some, not just most, but every single one.
CONTRAPOSITIVE Lesson 11 of 40
• J→ F
/F → /J
All J use the F = If you’re a J then you use the F
Contrapositives will save your life on the LSAT. Often, you’ll think you got an answer choice right. “Duh, they want me to infer that ‘All business school students are greedy.’ Hmm… but I don’t see it. WHAT IS GOING ON LSAT?!” Well, that’s because the right answer choice says “If you’re not greedy, you’re not a business school student.” See, same thing! I mean that too. Contrapositives are logically equivalent statements. You can think of them as being genetic twins. They’re the same.
To get from one statement in Lawgic to its contrapositive, you apply a two step transformation process.
Step 1. Switch the two symbols around the arrow.
Step 2. Slap a negation sign on each symbol.
Step 3. There is no Step 3. It’s a two step process.
You have to remember that when you slap a negation onto a symbol that’s already negated, the negation goes away. Negating “not selfish” becomes “selfish.”
CONTRAPOSITIVE MISTAKES Lesson 12 of 40
There are not contrapositives
When you do only one of the two steps for getting a proper contrapositive. You have to do both.
(1) Flip J→F --- F→J
(2) Negate /F→/J-- /J →/F
THE NEGATION Lesson 13 of 40
When we say “negation” – the “/” in Lawgic – we mean something very specific. What we mean is the contradiction. The logical opposite. What we mean is “it’s not the case that…”
*Negation is to find the binary cut. we’re speaking of contradiction.
Ex: Cold = not cold
BASIC TRANSLATION: GROUP 1 Lesson 16 of 40
IF, WHEN, WHERE, ALL, THE ONLY, EVERY, ANY, WHENEVER, ANYONE
BASIC TRANSLATION: GROUP 2 Lesson 19 of 40
ONLY, ONLY IF, ONLY WHEN, ONLY WHERE, ALWAYS, REQUIRES, MUST
BASIC TRANSLATION: GROUP 3 Lesson 22 of 40
UNLESS, UNTIL, OR, WITHOUT
BASIC TRANSLATION: GROUP 4 Lesson 27 of 40
NO, NONE, NOT BOTH, NEVER, CANNOT
NEITHER NOR Lesson 30 of 40
Neither nor = Not one and not the other
EX: Neither the pandas nor the koalas are cute enough to enter the zoo for free
*The pandas are not cute enough to enter the zoo for free and the koalas are not cute enough to enter the zoo for free
• Pandas –> not cute enough to enter
• Koalas –> not cute enough to enter
EX: Jane will neither select the blue dress nor the black dress
*Jane will not select the blue dress and Jane will not select the black dress
• Blue dress –> Jane not select
• Black dress –> Jane not select
MISCELLANEOUS LOGICAL INDICATORS Lesson 32 of 40
“IS ESSENTIAL” AND “IS REQUIRED” AND “IS NECESSARY”
The phrases “is essential” and “is required” and “is necessary” are predicates. They point to their subjects and say that those subjects are essential, are required, are necessary.
EX: Happiness is essential to living a good life.
What’s essential? Happiness. So, Happiness is the necessary condition.
• gl –> H
/H –> /gl
EX: Practice is required to be a skilled artist.
What’s required? Practice. So, Practice is the necessary condition.
• sa –> P
/P –> /sa
“is/are”
The verbs “is” and “are” have so many meanings and usages that you can write dissertations on them. Of course, not every usage of “is/are” means that we’re in conditional logic territory. But, some usages do signal exactly that.
EX: Cows are big.
• C –> b
/b –> /C
INVALID ARGUMENT FORM 1 of 7 Lesson 2 of 38
Common Invalid Argument forms
Valid = must be true
[English]
All Jedi use the Force. Darth Vadar uses the force. [Premises]
Therefore, Darth Vadar is a Jedi. [Conclusion]
LAWGIC
A →B
B
________
A
J→F
Fdv
_______
Jdv
INVALID ARGUMENT FORM 2 of 7 Lesson 3 of 38
Common Invalid Argument forms
[English]
All stars are beautiful. Orchids are not stars. Therefore, orchids are not beautiful.
LAWGIC
A→B
/A
_______
/B
S→B
/So
_______
/Bo
INVALID ARGUMENT FORM 3 of 7 Lesson 4 of 38
Common Invalid Argument forms
[English]
All dogs are cute. Some cute things are lovable. Therefore, some dogs are lovable.
LAWGIC
A→B some C
_______________
A some C
INVALID ARGUMENT FORM 4 of 7 Lesson 5 of 38
Common Invalid Argument forms
[English]
All taxi drivers are men. Most men like hate driving. Therefore, most taxi drivers hate driving.
LAWGIC
A→B—most-->C
__________
A—most--> C
**You will find this in Parallel Flaw question types!**
INVALID ARGUMENT FORM 5 of 7 Lesson 6 of 38
Common Invalid Argument forms
[English]
Some dishes in the castles are antiques. Some antiques are worth a lot of money. Therefore, dishes in the castles are worth a lot of money.
LAWGIC
A some B some C
________
A some C
D some A some MW
__________
D some MW
INVALID ARGUMENT FORM 6 of 7 Lesson 7 of 38
Common Invalid Argument forms
[English]
Most runners buy running shoes. Most people who buy running shoes don’t like to run. Most runners don’t like to run.
LAWGIC
A—most-->B—most--> C
_______________________________
A—most--> C
R—most-->B—most-->/L
_________
R—most--> /L?
Most runners buy running shoes. Most people who buy running shoes don’t like to run. Some runners don’t like to run.
LAWGIC
A-most->B-most->C
_____
A some C
INVALID ARGUMENT FORM 7 of 7 Lesson 8 of 38
Common Invalid Argument forms
[English]
Some astronauts are brave. Some astronauts are smart. Therefore, some astronauts are brave and smart.
LAWGIC
A some B
A some C
________
B some C
VALID: Affirming the sufficient, negating the necessary, existential before universal serial argument strings
INVALID: Affirming the necessary, negating the sufficient, universal before existential serial argument strings.
One thing I’ve noticed is that argument forms can be characterized as having either a parallel construction or a serial construction. I’m defining serial construction as when one idea has some direct relationship with the other ideas (e.g.: A –> B –> C). I see parallel construction to be when the relationships between two ideas are indirectly linked through a third idea (e.g.: A –> B; A –> C).
An easy rule I’ve found is that serial argument forms are only valid when Some/Most is before Implies (or the existential are before the universal qualifiers).
Interestingly, of the five possible parallel argument forms, only one parallel form (#7) is invalid.
JY’s NOTES
THESE INVALID ARGUMENT FORMS APPEAR OFTEN.
Invalid form 1 of 7
Affirming the Necessary
[English] All Jedi use the Force. Dooku uses the Force. Therefore, Dooku is a Jedi.
[Lawgic] A –> B
B
_________
A
You don’t know what else, in addition to Jedi, also uses the Force. So, just because something is in the B (Force user) category doesn’t make it an A (Jedi). It could be an A, but it doesn’t have to be. Turns out, Dooku is a Sith Lord.
Invalid form 2 of 7
Denying the Sufficient
[English] All tragedies are sad. I’m not a tragedy. Therefore, I’m not sad.
[Lawgic] A –> B
/A
_________
/B
Even though I’m not a tragedy… I could still be sad. What if I just found out that someone ate my pet turtle? I’d be very sad.
Invalid form 3 of 7
[English] All dogs are cute. Some cute things are lovable. Therefore, some dogs are lovable.
[Lawgic] A –> B some C
_________
A some C
So all A’s are B’s and some B’s are C’s. Which B’s are C’s? There could be plenty of B’s that are not A’s and it’s those non-A-B’s that are C’s. So it certainly isn’t a necessity that some A’s are C’s.
That was the abstract explanation. Here’s something more tangible. I always use mental pictures to help me with this. Let’s make the first premise true. So, imagine a bucket containing dogs. Now, take that bucket and drop the whole thing into a larger bucket labeled cute things. We’ve just made the first premise true. Now, let’s make our second premise true. We’re going to reach into the bucket of cute things and grab a handful of what’s in there and toss it into the bucket of lovable things. Isn’t it possible that in our handful, we’ve failed to grab any dogs? In other words, we’ve only grabbed the non-dog cute things? That’s why the argument isn’t valid. Because it could be the case that there are no dogs that are lovable.
Invalid form 4 of 7
[English] All A’s are B’s. Most B’s are C’s. Therefore, most A’s are C’s
[Lawgic] A –> B -most-> C
_________
A -most-> C
The explanation for this is the same as in form 3.
Invalid form 5 of 7
[English] Some A’s are B’s. Some B’s are C’s. Therefore, some A’s are C’s
[Lawgic] A some B some C
_________
A some C
Say we have some computers that are amazing. There are some amazing things that are edible. Does that mean there must be some computers that are edible? No. In fact, we know that no computers are edible.
Invalid form 6 of 7
[English] Most A’s are B’s. Most B’s are C’s. Therefore, some A’s are C’s
[Lawgic] A -most-> B -most-> C
_________
A some C
Let’s say that most cats are mammals. It’s true. It’s also true that most mammals are not cats. Does it follow that some cats are not cats? This is not a valid argument form.
As a corollary and since the “some” statement is weaker than the “most” statement, the following arguments are also invalid:
A -most-> B some C
_________
A some C
A some B -most-> C
_________
A some C
Invalid form 7 of 7
[English] Some A’s are B’s. Some A’s are C’s. Therefore, some B’s are C’s
[Lawgic] A some B
A some C
_________
B some C
This one is exactly the same as form 5 because “some” is reversibly read. This form can be read as:
C some A some B
Now, in form, it’s exactly like form 5.
EXISTENTIAL QUANTIFIERS OVERVIEW Lesson 1 of 30
• Existential quantifiers are intersectional relationships. Some X are Y (X some Y).
• He says that universal quantifiers talk about complete subsumpion– in other words, completely subsumed and contained. All X must be Y (X–>Y).
o No contrapositives
RELATIONSHIP TO UNIVERSAL QUANTIFIERS Lesson 2 of 30
• Conditional logic =UQ
• UQ: learning about a relationship of complete subsumption – where 2 groups of things existed where 1 group is completely subsumed by another group (Jedi & Force users) and (watermelon subsumed by fruit-Sufficient Condition & Necessary Condition)
• Existential quantifiers
Relationship – intersection instead of 1 group being completely subsumed by another group we have 2 groups that happen to share some share of overlap
Ex: Venn diagram – size of intersection between the relation of one idea and another idea (dogs & things that are cute)
• Describes the difference between Some & Most relationships
EXISTENTIAL QUANTIFIERS BRIEF Lesson 3of 30
• There exist things such as ______ (fill in the blank- predict)
Ex: happy people v. poor people (middle intersection)
• Indicators: “SOME”
• **No such thing as a contrapositive- it does NOT exist for EXISTENTIAL QUANTIFIERS
“SOME” STATEMENTS MEANING Lesson 4 of 30
• EQ
• "Some speaks of a range”-> “All speaks of a point (100)”
• Definition of “some” is at least 1
• Starts at 1 to 100 (does not include 0)
• Ex: Some dogs are playful (1-100) → all dogs are playful (100)
• Lower bound: 1
Upper bound: 100
• 0 is not included in Some
“SOME” STATEMENTS TRANSLATE Lesson 5 of 30
• [Some] dogs (D) are cute (C)
D some C
*Some is an intersection that’s why it does not carry an arrow
• NO SUCH THING AS A CONTRAPOSITIVE =/= /D some /C- YOU KNOW TOO LITTLE TO DETERMINE IF (NON-DOGS ARE NOT CUTE? HOW DO YOU KNOW? YOU DON’T KNOW!)
“MANY” = “SOME” Lesson 6 of 30
• On the LSAT, the word “many” just means “some”
“MOST” STATEMENTS MEANING Lesson 7 of 30
• Existential Quantifier
• Intersection between two ideas
• Definition for “Most” is half plus 1
• Lower bound: 51
Upper bound: 100
• Also speaks of a range
• Ex: Most cats are furry
At least 51 of the cats are furry.
“MOST” STATEMENTS TRANSLATION Lesson 8 of 30
• Ex: [Most] Pandas (P) like to eat bamboo (EB)
More than half of the pandas like to eat bamboo
P---most-- >E
**Direction of the arrow does matter-
*”Most” is the subset of “some”
• NO CONTRAPOSITIVES!
“FEW” STATEMENTS MEANING AND TRANLATION Lesson 9 of 30
• EQ
• Definition of “few” is some are, most are not
• Ex: [Few] dogs (D) are evil (E)
1. Some dogs are evil – D some E (and)
2. Most dogs are not evil- D –most-- > /E
• On the LSAT "few" focuses on MOST ARE NOT
ADVANCED: ALL IMPLIES MOST IMPLIES SOME Lesson 10 0f 30
• All implies Most implies Some
• All → Most → Some
• All → Some
• All is the most restricted – it’s just a point
• Ex: All pencils are made from trees
Most pencils are made from trees – P –most-- > T
Some pencils are made from trees – P some T
INTERSECTION RELATIONSHIPS Lesson 11 0f 30
• WHAT’S AN EXISTENTIAL QUANTIFIER? First, understand that just like the conditional relationships, this idea also expresses a relationship. Whereas the conditional relationship expresses the idea that one group is being completely subsumed by another group, here, with the existential quantifier, we’re talking about a different kind of relationship. We’re talking about the relationship of intersections. There are two types of intersection relationships.
• The three logical indicators here are “some” which means at least 1 up to all; “most” which means half plus 1 up to all; and “few” which usually means some are and most are not.
INTERSECTION TRANSLATIONS Lesson 12 0f 30
TRANSLATIONS TO LAWGIC FOR INTERSECTION STATEMENTS:
• The “Some” Group: some, many, several, at least one, lots, not none
• The “Most” Group: most, a majority, more than half
• The “Few” Group: few
**Remember that there are no contrapositives for these intersection relationships. They don’t exist. You can try to get a “contrapositive” for these statements and you’ll see that they don’t express the same idea at all. For each of these statements, there is just one way in Lawgic to express them.
ADVANCED: NEGATE SOME STATEMENTS Lesson 13 0f 30
• Some – None
• Ex: Some dogs are brave
D some B
• Negate [No] dogs are brave
D→ /B
B→ /D
• All- Some Not
ADVANCED: NEGATE ALL STATEMENTS Lesson 14 0f 30
• All- Some… Not… (0-99)
• Ex: All cats(C) are pretentious (P)
C→P
• Negate: [Some] cats are [not] pretentious
C some /P
DENY THE RELATIONSHIP Lesson 15 of 30
• A→ B (all statement)
To deny this statement the arrow cannot happen
A is the S.C & B is the N.C
Then you must deny the arrow
• A some /B
• A and /B
HOW TO NEGATE STATEMENTS IN ENGLISH Lesson 16 of 30
• Negating the Conditional Sentence
To negate a conditional statement, you should realize that what you’re negating is the conditional relationship. In other words, where the original statement says that A and B exist in a conditional relationship, you’re saying that no, A and B do not exist in a conditional relationship. That A is not sufficient for B and B is not necessary for A. For example, negate this statement:
o All Jedi use the Force.
Did you say “No Jedi use the Force?” That’s not right. To negate this statement, you’re denying the conditional relationship between the categories Jedi and Force users. Whereas the original statement is stipulating that the categories of J and F exist in a conditional relationship, you’re saying J is not sufficient for F (and F is not necessary for J). So, in English, it becomes an intersection statement.
o Some Jedi do not use the Force.
See how that’s different from “No Jedi use the Force?” That’s how it works for all conditional statements. You can formulate the contradiction (i.e., the negations) by saying “Some [of the sufficient] is not [the necessary].” Or, if grammatically it doesn’t make sense to use “some,” you can fall back on the more general rule of “One can be [the sufficient] and not be [the necessary].” For example, “If the President endorses this bill, then it will pass.” Here, it clearly doesn’t make sense to use “some.” So, we fall back on the more general rule and say “The President can endorse the bill and it could not pass.”
• Negating the Intersection Sentence
You should have some idea of how to contradict intersection statements by now. It’s just the reverse of the rule for contradicting conditional statements. You are denying the fact that an intersection relationship exists between the two groups. For example:
Some cats are furry.
The contradiction is that there is no intersection between cats and furry things. “No cats are furry” or “All cats are not furry.” You replace the “some” with a “no.” Alternatively, you can replace the “some” with an “all… not.” Let’s look at another example:
Sometimes, when I eat too much ice cream, I get a stomachache.
The contradiction is “I never get a stomachache from eating too much ice cream.” Or, “Whenever I eat too much ice cream, I do not get a stomachache.”
For now, if you need to rely on these translation mechanisms, that’s okay. You’re training your intuition so that one day, you can tag the clause “it’s not the case that…” in front of any sentence and understand what the negation of that sentence is.
Logical Opposites Range Construction Example
All 100 All... are... All cats are pretentious.
Not all 0-99 Some... are not... Some cats are not pretentious.
Logical Opposites Range Construction Example
Some 1-100 Some... are... Some dogs are brave.
None 0 No... are... No dogs are brave.
ASSUMPTIONS Lesson 1 of 21
WHAT ARE ASSUMPTIONS?
Simply put, they are premises that the author has left out of the argument. That is all assumptions are, period. It’s a forgotten premise that is left out.
Assumptions are VERY subtle! Therefore you have to be careful!
EX: We’ll get to the theater in time to catch the show[C] because we’re going to take a cab [P].
A1: There are cabs a plenty
A2: It is not raining
A3: There’s no traffic jam
If you deny these assumptions then they weaken the argument.
DO NOT ATTACK THE PREMISE OR CONCLUSION; ATTACK THE SUPPORT! YOU ARE TO ACCEPT ALL OF THE ANSWER CHOICES.
HOW TO WEAKEN ARGUMENTS Lesson 6 of 21
**On Weakening questions the focus is on the SUPPORT not the premise or conclusion---ATTACK the SUPPORT not the P or C on every Weakening question.
SOME SAMPLE QUESTION STEMS
Which one of the following, if true, is the logically strongest counter that Albert can make to Erin’s argument?
Which one of the following statements, if true, most weakens the argument?
Which one of the following, if true, most weakens the argument?
Which one of the following, if true, most seriously undermines the conclusion drawn in the argument above?
Which one of the following, if true, would most weaken the argument in the newspaper article?
VALIDITY Lesson 1 of 14
DEFINITION OF VALIDITY: If (or pretend that) the premises are all true, then the conclusion must also be true.
-Validity is a very special relationship between premises and the conclusion. Validity is the strongest of the support relationships. An argument that makes zero assumptions is valid.
-The definition of a valid argument:
If the premises are true, then the conclusion must also be true.
VALID ARGUMENTS FORM (1 OF 9) Lesson 4 of 14
Common Valid Argument Forms: Affirming the Sufficient Condition
All boys like to play computer games.
Tom is a boy.
Therefore, Tom likes to play computer games.
A→ B
A (Premises)
_____
B (Conclusion)
VALID ARGUMENTS FORM (2 OF 9) Lesson 6 of 14
-Common Valid Argument Forms: Denying the necessary condition
All doctors treat patients.
Hercules does not treat patients.
Therefore, Hercules is not a doctor.
A→ B
/B
_____
/A
VALID ARGUMENTS FORM (3 OF 9) Lesson 8 of 14
Common Valid Argument Forms: The Transitive
Everyone has capacity to love. (A →
Having the capacity to love requires compassion. (B→ C)
Therefore, everyone has compassion. (A → C)
A→ B → C
____________
A → C
How to Approach Must be true questions Lesson 11 of 14
INFERENCE: MUST BE TRUE (MBT) QUESTIONS.
-The majority of these questions use formal logic, i.e., they contain conditional or intersection statements.
-Your understanding of validity is tested here. For these MBT questions, you are asked to select an answer choice such that when the statements in the stimulus are true, the right answer choice must also be true. In other words, your task is to formulate a valid argument.
-YOU WILL FIND THE CONCLUSION IN THE ANSWER CHOICE. ACCEPT THE STIMULUS.
-Very much like the MSS questions, the MBT questions also take information from the stimulus and forces it down into the answer choices to prove one of them correct. The standard of proof is higher for these questions than for MSS questions.
-Doing these questions