Lesson Two: Logic Games, Logical Reasoning, & Reading Comprehension Flashcards
–LOGIC GAMES & LOGICAL REASONING–
Logical Opposite
divides subject into two separate parts.
e.g. Logical Opposite of Hot = NOT Hot
Two state something as a _______________ _______________ you add “_______” ahead of the subject / term.
logical opposite; NOT
If Not Hot is the logical opposite of Hot, then why is it wrong to say that “cold” is the logical opposite of hot?
cold is a polar opposite.
Not Hot is the opposite (answer) that covers the entire range of other temperatures that are the opposite of hot (lukewarm, tepid, cold etc.)
Polar Opposite
Involves dividing a subject on a spectrum.
Logical Opposites – Quantity
All: give quantity (%) and logical opposite
Some: give quantity (%) and logical opposite
All: 100%
Not All: 0-99%
Some: 1-100% (everything but none)
None: (Not Some = Not at least 1 = 0 = None) 0%
So we know “______” and “________” are _____________ opposites (at two extremes of a pole), and there are several quantities that operate on a _______________ between them. However, “______” and “______ _________”, and “________” and “__________” are “__________” opposites.
All; None; polar; spectrum; All; Not All; Some; None
Logical Opposition – Time
Always: give quantity (%) and logical opposite
Sometimes: give quantity (%) and logical opposite
Always: 100% all the time
Not Always: 0-99% of the time
Sometimes: 1-100% of the time
Never: 0% of the time
Logical Opposition – Space
Everywhere: give quantity (%) and logical opposite
Somewhere: give quantity (%) and logical opposite
Everywhere: 100% in all places
Not Everywhere: 0-99% of places
Somewhere: 1-100% of places
Nowhere: 0% of places
State the Equivalences of Logical Opposites across Space and Time
Always Everywhere
]—————————[
Not Always Not Everywhere
Sometimes Somewhere
]—————————[
Never Nowhere
The Opposition Construct: Truth and Falsity
False: True
Cannot Be False = Must Be True
Could Be False = Not Necessarily True
Not Necessarily False = Could Be True
Must Be False = Cannot Be True
A trend we’re seeing here is that in ________________ there are logical _____________, but in _________________ there are logical ________________.
verticality; opposites; horizontality; equivalences.
Don’t waste time trying to answer a question under _________________. Save ______________ can covert the _____________ to a question under _______________.
falsity; time; falsity; truth
Example: If you have a problem asking you “Which one of the following could be false?” how should you really answer this question.
Could Be False –> logical opposite = Could Not Be False = Not Necessarily True
“Which one of the following is not necessarily true?”
Sufficient Condition
term that requires a necessary condition to occur.
Necessary Condition
term that is required for the sufficient condition to occur.
“If you get an A+, then you must have studied.”
Identify the sufficient and necessary condition.
Sufficient Condition: getting an A+
Necessary Condition: you studied
If the ________________ condition happens, you know the _____________ must also occur. However, the occurrence of the _____________ condition does not mean the ________________ condition has to occur (it MAY but it doesn’t have to).
sufficient; necessary
Explain what your conditional rules should look like when diagramming.
The sufficient condition should be on the left, the necessary condition should be on the right.
Mistaken Reversal
(“If you get an A+, then you must have studied.”)
Says the necessary condition is required for the sufficient condition to occur.
E.g. If you studied, then you will get an A+
–> You studying doesn’t guarantee you’ll get an A+.
Mistaken Negation
(“If you get an A+, then you must have studied.”)
Says if the sufficient condition doesn’t occur, then the necessary condition doesn’t occur.
E.g. If you didn’t get an A+, then you must not have studied.
–> I could’ve very well studied and still gotten a different grade.
Contrapositive
(“If you get an A+, then you must have studied.”)
If the necessary condition didn’t occur, the sufficient condition didn’t occur (flip and negate).
E.g. If you didn’t study, then you didn’t get an A+
̶st̶u̶d̶y̶ → ̶A̶+̶
Sufficient Condition Indicators
if
when
whenever
every
all
any
people who
in order to
“the only”
Necessary Condition Indicators
then
only
only if
must
required
*unless
*except
*until
*without
Using the rules we’ve learned thus far, diagram the sentence, “Whenever the President flies, he uses Air Force One.” Also give it’s contrapositive
Whenever –> sufficient condition indicator
“Whenever the President flies”: P
“he uses Air Force One”: AF1
P→AF1
Contrapositive: A̶F̶1̶ → ̶P̶
Explain Chain Relationships.
Provide an example using A/B, B/C, a chain relationship, an inference, and its contrapositive.
If the same variable is the necessary condition in one sentence, and the sufficient condition in another sentence, then the two sentences can be conjoined because the variable links them together.
Statement 1: A→B
Statement 2: B→C
Chain Relationship: A→B→C
Inference: A→C
Contrapositive: ̶C̶ → ̶B̶ → ̶A̶
Explain the Unless Equation
If the words “unless,” “until,” “except,” and “without” modify a term within a conditional sentence, that term becomes the necessary condition, AND the other term is negated and becomes the sufficient condition.
Unless Equation Example Problem: “Unless a person studies, he or she will not receive an A+.”
Unless modifies “a person studies” (Study), so it will become the necessary condition.
Therefore, “he or she will not receive an A+” will be negated and made the sufficient condition.
A+ → Study
Multiple Sufficient and Necessary Conditions
On the LSAT there are going to be conditional statements where there are multiple sufficient conditions and multiple necessary conditions.
Multiple Sufficient and Necessary Conditions: “And”
“And” indicates that two requirements in a conditional statement are BOTH necessary conditions.
Multiple Sufficient and Necessary Conditions: “Or”
“Or” indicates that between two requirements in a conditional statement, only ONE is a necessary condition.
Multiple Sufficient and Necessary Conditions Example: Diagram This –> “To be elected President of the United States, you must be at least 35 years of age and a natural born citizen of the United States.”
Pay attention to everything: “must be” modifies “at least 35 years of age and a natural born citizen of the United States,” so it is the necessary condition.
there are 2 requirements to be president indicated by the AND, which we will represent using “+.”
35
P → +
NBC
Multiple Sufficient and Necessary Conditions Example: Diagram the Contrapositive of “To be elected President of the United States, you must be at least 35 years of age and a natural born citizen of the United States.”
Both being 35 AND being an NBC are requirements for presidential eligibility. If even ONE of these requirements are not met, then you can’t be President.
̶3̶5̶
or → ̶P̶
̶N̶B̶C̶
When taking the contrapositive of a condition, the “________” becomes an “____.”
and; or
When taking the contrapositive of a condition, the “_____” becomes an “_____.”
or; and
Double Arrows
aka “Biconditional”
Double arrows represent when the variables in a conditional statement are both the necessary and sufficient condition.
Indicator word/phrase for Double Arrows?
“if and only if”
“if but only if”
“when and only when”
Double Arrows Example Problem: “Ann will attend if and only if Basil attends.”
Ann will attend if Basil attends: B → A
Ann will attend only if Basil attends: A → B
Biconditional relationship: A ↔ B
Contrapositive: ̶B̶ ↔ ̶A̶
–THE READING COMPREHENSION SECTION–
How many questions and how long do you have to complete the Reading Comprehension section?
You have 35 minutes to complete 26-28 questions.
You’ll be presented with 5 readings:
- 3 long passages
- 2 (comparatively) shorter passages
You’ll have exactly 8 min 45 sec to complete each passage and their corresponding questions.
How long should it take you to read a given passage?
2 minutes.
(But since, we’re not all that experienced yet, we’ll practice 2.5-3 minutes).
REMINDER: Reading too slow or too fast will put you at a major disadvantage. You will either be left with no time to answer the questions because you read to slow, or you will have skimmed over important information by reading to fast, forcing you to circle back and re-read.
READ ______________ THAN WHAT’S IMMMEDIATELY COMFORTABLE, AND DO NOT _________________ PASSAGES.
FASTER; RE-READ
Use only the ______________ in the ______________ to answer the questions to the reading passages.
information; passages
! 5 Critical Elements You Must Track When Reading Passage !
- VIEWpoints in the passage.
- Structure of the passage.
- Tone of the passage.
- Attitude of each individual/group.
- Main Point of the passage.
These 5 critical elements are what we otherwise know as ______________, and tracking each of these elements through the passage will make answering questions a lot _____________.
VIEWSTAMP; easier
Be sure to track __________________ (____________ and ______ _________________) through the passage. It will help you understand the flow of the passage. Many of these Reading Comprehension passages are designed to seem clustered and dense with alot of intertwined information from the author’s view and competing subject’s view. Tracking the view points allows you to “________________” this info and parse up the passage into the different viewpoints without getting ________________. (A possible helpful trick is to write “VP1,” “VP2,” “VP3” next to separate viewpoints)
viewpoints; competing; noncompeting; untangle / unravel; lost
Common Text Based Indicators (things to look out for in the passages):
Initial Information / Closing Information
Many of the questions after the passage are related to the information at the very start and end of the passage.
Pay close attention to the first five and last five lines of the passage.
Common Text Based Indicators (things to look out for in the passages):
Difficult Words, Phrases, or Concepts
Test takers just put these in here to confuse you.
Don’t waste time trying to define them.
Work to understand what these words mean in the greater context, and for the greater understanding, of the reading.
Common Text Based Indicators (things to look out for in the passages):
Dates and Numbers
Date and numbers are useful for tracking chronology in passages.
(make sure that dates mentioned in a passage coincide with their respective event).
Common Text Based Indicators (things to look out for in the passages):
Definitions
Take note of definitions that are given in the passage. It’s more likely than not that you will be questioned based on your understanding of the definitions.
Common Text Based Indicators (things to look out for in the passages):
Enumerations / List
If there was a decision made in the passage, and there is a list of reasons as to why that decision was made (premises), be ready to answer questions based on these list of points.
“First…Second…Third”
“First…Second…In Addition…”
“First…Second…Third…Finally…”
“(1)…(2)…”
“Initially…And…Further…”
“One possibility is…another possibility…A final possibility…”
If you are presented with a list, then write ___, ___, ___ next to wherever the items of the list are.
1; 2; 3
Common Text Based Indicators (things to look out for in the passages):
Examples
Used to illustrate a hard-to-understand / abstract concept.
If you see an example the author (etc.) is using to convey a point / definition, then write “____” next to it.
ex.
Common Text Based Indicators (things to look out for in the passages):
Hidden References
If a topic is mentioned in one area of the passage, and ANOTHER area of the passage, be prepared to answer a question based on the topic.
You will have a question that refers to the topic’s first appearance in the passage, but oftentimes, the information needed to answer the question can be found where the topic is mentioned next.
Common Text Based Indicators (things to look out for in the passages):
Text Questions
Track text questions, because they’re usually answered immediately after they’re presented (by the author), and it gives the reader a framework for where the author is going next in the passage.
The Location Element
Where in the passage you should begin searching for the correct answer.
Types of Location (3) in the Question Stem:
1) Specific Reference
2) Concept Reference
3) Global Reference
Specific Reference
Question Stems that relate to specific word, phrase, Sentence, paragraph
“The author of the passage uses the phrase “________…” in the third paragraph primarily in order to…”
Concept Reference
Question Stems that ask about ideas that were clearly enunciated, but not explicitly stated, in the text.
“Ideas in the passage that are not specifically identified in a phrase or paragraph.”
“The author’s discussion of _________________ primarily serves to…”
Global Reference
Question Stems about the passage as a whole / lack specificity about any particular thing regarding the passage.
“Which of the following most accurately expresses the main point of the passage.”
Just like the Logical Reasoning section, you need to ________________ your _______________. You will never feel comfortable picking an answer until you can find absolutely ______ reason to ________________ the answer.
Take a couple of ______________ before diving into your answer choices and, based your knowledge from the reading and question presented, think about what the answer should ___________ like. This way, you can more easily _______________ wrong answer choices.
prephrase; answers; no; dismiss; seconds; look; wrong
