Diagram Flashcards
D is inspected two days before E
G marches three groups behind F
There are three spaces between L and M, and M is examined before L
How do you diagram
J and H cannot be selected together?
It depends on whether it is a linear or a group game
Double Not Arrow means the two terms can never be together
(Grouping Question)
inference – double not - important for grouping
Attach two statements
Arun will be selected if and only if Bai is selected
if and only if creates two seperate conditional statements
- A if B
- A only if B
Only two scenarios are possible under a double arrow
- A and B are selected
- Neither A nor B is selected
Double Arrow
Only two scenarios are possible under a double arrow
- A and B are selected
- Neither A nor B is selected
Introduced in three ways
- If and only if - or its variants - if but only if - or - if yet only if
- Vice Versa (as in “If A is selected then B is selected and vice versa”)
- By repeating and reversing the terms (“If A is selected then B is selected, and if B is selected then A is selected”)
(Can be made through if and only if)
if and only if creates two separate conditional statements
- A if B
- A only if B
S is not selected if R is not selected
(And contrapositive)
There are two days between the day Q is inspected and the day R is inspected
There are two spaces between Q and R
F is displayed immediately prior to G, and is displayed at some point before I
Whatever term is modified by unless, except, without, until becomes the ….
Necessary Condition
The other term is negated and becomes the sufficient condition
Unless a person studies, they will not recieve an A
study –> A
S is not fourth unless T is fifth
S4 –> T5
Whatever term is modified by unless, except, without, until becomes the Necessary Condition
The other term is negated and becomes the sufficient condition
Unless a person studies, they will not recieve an A
study –> A
Laron performs second only if Nancy performs sixth
If V is displayed immediately before W, then S must be displayed third
If K is first then M is before P
G does not speak fourth unless Q speaks second
Only desginates a
necessary condition… just like only if
Only zombies eat brains
Eat brains > Zombie
-
only designates necessary condition
Only if designates
necessary condition
Only if one is starving it is acceptable to eat a slim jim
n and s?
slim jim > starving
-
only if desginates necessary
With “If and only if” statements what are the only two conditions
Either both conditions occur or neither one does
Diagram
No man wears perfume
man > -perfume-
no always negates the second term
Diagram
No A’s are B’s
A > -B-
no always negates the second term
Diagram and Contra
If the professional wrestler is in the ring, then he is wearing knee pads or a spandex body suit, but not both
Diagram and Contra
If the professional wrestler is in the ring, then he is wearing knee pads or a spandex body suit, but not both
-
-
contra
If the wrester is wearing neither knee pads nor a spandex suit, or if he is wearing both knee pads and a spandex body suit, then he is not in the ring
What deductions can you make from two most statements
- Most NFL players are incredibly fast
- Most NFL players weigh over 250 pounds
The only deduction you can make is if two most statements share a suffiient condition, in which case a some connection is produced
-
-
- Most NFL players are incredibly fast
- Most NFL players weigh over 250 pounds
-
Some of those who are incredibly fast weigh over 250 pounds
Deductions
-
- Most NFL players are incredibly fast
- Most NFL players weigh over 250 pounds
The only deduction you can make is if two most statements share a suffiient condition, in which case a some connection is produced
-
-
- Most NFL players are incredibly fast
- Most NFL players weigh over 250 pounds
-
Some of those who are incredibly fast weigh over 250 pounds
Deductions?
-
All of the members of the circus perform high-wire acts,
Some members of the circus do not have life insurance
Some people who perform high-wire acts without life insurance
-
With All + Some statements, the shared term must be the sufficient condition of the all statement
With All + Some statements ….
To make a deduction with All + Some statements, the shared term must be the suffifient condition of the all statement
If all A’s are B’s and Some A’s are C’s, then Some B’s are C’s
If all A’s are B’s and Some A’s are C’s, then ….
If all A’s are B’s and Some A’s are C’s, then Some B’s are C’s
To make a deduction with All + Some statements, the shared term must be the sufficient condition of the all statement
With All + Most statements…
There are two ways of combining All + Most statements,
-
If the necessary condition of the Most statement is the sufficient condition of the All statement, then you can produce a Most statement as the conclusion
If they share the same sufficient condition, then you can only produce a some statement
When combining an All + Most statements,
If the necessary condition of the Most statement is the sufficient condition of the All statement, then…
There are two ways of combining All + Most statements,
-
If the necessary condition of the Most statement is the sufficient condition of the All statement, then you can produce a Most statement as the conclusion
If they share the same sufficient condition, then you can only produce a some statement
When combining an All + Most statements,
If they share the same sufficient condition, then you can only produce a some statement
-
If the necessary condition of the Most statement is the sufficient condition of the All statement, then you can produce a Most statement as the conclusion
Most Hannah Montana fans wear skinny jeans.
All Hannah Montana fans are 12 year old girls
Combine..
Some of those who wear skinny jeans are 12 year old girls
When combining All + Most:
If they share the same sufficient condition, then you can only produce a some statement
If the necessary condition of the Most statement is the sufficient condition of the All statement, then you can produce a Most statement as the conclusion
Combining two Most statements
The only time you can derive a conclusion from two most statements is when they share the sufficient condition
–
If most A’s are B’s and most A’s are C’s, then some B’s are C’s
If most A’s are B’s and most A’s are C’s, then ..
The only time you can derive a conclusion from two most statements is when they share the sufficient condition
–
If most A’s are B’s and most A’s are C’s, then some B’s are C’s
Combining two Some statements
Two Some statements can never lead to a valid conclusion
also
A Most and a Some can never lead to a valid conclusion
Combining a Most and a Some Statement
A Most and a Some can never lead to a valid conclusion
also
Two Some statements can never lead to a valid conclusion
Principle of Distribution
In Ordering games, a Principle of Distribution restricts how many slots a player can fill or how many players can be assigned to a slot
In Ordering games, a ………… restricts how many slots a player can fill or how many players can be assigned to a slot
In Ordering games, a Principle of Distribution restricts how many slots a player can fill or how many players can be assigned to a slot
Family #1, Must Be or PROVE Family
-
- Must Be True
- Main Point
- Point at Issue
- Method of Reasoning
- Flaw in the Reasoning
- Parallel Reasoning
-
The First Question Family is based on the principle of using the information in the stimulus to prove that one of the answer choices must be true
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Stimulus accepted as given while the answer choices are “under suspicion,” and the information in the stimulus is used to prove one of them.
-
Rules
1. The information in the stimulus is suspect. There are often reasoning errors present, and you will further weaken the argument in some way.
-
2. The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best attacks the argument in the stimulus.
Family #2, Help Family
-
- Assumption
- Justify the Conclusion
- Strengthen/Support
- Resolve the Paradox
-
Rules
1. The information in the stimulus is suspect. There are often reasoning errors present, and depending on the question, you will help shore up the argument in some way.
-
- The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best meets the question posed in the stem.
Family #3, Hurt Family
-
consists of one question type:
Weaken
-
Compared to the Second Question Family, the Help family, the only difference between the diagrams is that the third family diagram has a bar across the arrow. This bar signifies a negative: instead of strengthening or helping the argument, you attack or hurt the argument.
-
Rules:
- ## The information in the stimulus is suspect. There are often reasoning errors present, and you will further weaken the argument in some way.
- The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best attacks the argument in the stimulus.
consists of one question type:
Cannot Be True
-
The 4th question family is based on the principle that you must use the information in the stimulus to prove that one of the answer choices cannot occur. Compared to the First Question Family, the only difference in the diagram is that the Fourth Family diagram has a bar across the arrow. Again, this bar signifies a negative
-
Rules
- ## You must accept the stimulus information—even if it contains an error of reasoning—and use it to prove that one of the answer choices cannot occur.
- Any information in an answer choice that does not appear either directly in the stimulus or as a combination of items in the stimulus will be incorrect. The correct answer choice will directly disagree with the stimulus or a consequence of the stimulus.
Family #1
Family #1, Must Be or PROVE Family
-
- Must Be True
- Main Point
- Point at Issue
- Method of Reasoning
- Flaw in the Reasoning
- Parallel Reasoning
-
The First Question Family is based on the principle of using the information in the stimulus to prove that one of the answer choices must be true
-
Stimulus accepted as given while the answer choices are “under suspicion,” and the information in the stimulus is used to prove one of them.
-
Rules
1. The information in the stimulus is suspect. There are often reasoning errors present, and you will further weaken the argument in some way.
-
2. The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best attacks the argument in the stimulus.
Family #2
Family #2, Help Family
-
- Assumption
- Justify the Conclusion
- Strengthen/Support
- Resolve the Paradox
-
Rules
1. The information in the stimulus is suspect. There are often reasoning errors present, and depending on the question, you will help shore up the argument in some way.
-
- The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best meets the question posed in the stem
Family #3
Family #3, Hurt Family
-
consists of one question type:
Weaken
-
Compared to the Second Question Family, the Help family, the only difference between the diagrams is that the third family diagram has a bar across the arrow. This bar signifies a negative: instead of strengthening or helping the argument, you attack or hurt the argument.
-
Rules:
- ## The information in the stimulus is suspect. There are often reasoning errors present, and you will further weaken the argument in some way.
- The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best attacks the argument in the stimulus.
Family #4
consists of one question type:
Cannot Be True
-
The 4th question family is based on the principle that you must use the information in the stimulus to prove that one of the answer choices cannot occur. Compared to the First Question Family, the only difference in the diagram is that the Fourth Family diagram has a bar across the arrow. Again, this bar signifies a negative
-
Rules
- ## You must accept the stimulus information—even if it contains an error of reasoning—and use it to prove that one of the answer choices cannot occur.
- Any information in an answer choice that does not appear either directly in the stimulus or as a combination of items in the stimulus will be incorrect. The correct answer choice will directly disagree with the stimulus or a consequence of the stimulus.
The …. Question Family is based on the principle of using the information in the stimulus to prove that one of the answer choices must be true
The First Question Family (Must Be or PROVE Family)is based on the principle of using the information in the stimulus to prove that one of the answer choices must be true
-
- Must Be True
- Main Point
- Point at Issue
- Method of Reasoning
- Flaw in the Reasoning
- Parallel Reasoning
-
Stimulus accepted as given while the answer choices are “under suspicion,” and the information in the stimulus is used to prove one of them.
-
Rules
1. The information in the stimulus is suspect. There are often reasoning errors present, and you will further weaken the argument in some way.
-
2. The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best attacks the argument in the stimulus.
The ……. Question Family is based on the principle of assisting or helping the author’s argument or statement in some way, whether by revealing an assumption of the argument, by resolving a paradox, or in some other fashion
The Second Question Family (Help Family) is based on the principle of assisting or helping the author’s argument or statement in some way, whether by revealing an assumption of the argument, by resolving a paradox, or in some other fashion
-
- Assumption
- Justify the Conclusion
- Strengthen/Support
- Resolve the Paradox
-
Rules
1. The information in the stimulus is suspect. There are often reasoning errors present, and depending on the question, you will help shore up the argument in some way.
-
- The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best meets the question posed in the stem
The …. Question Family asks you to attack the author’s argument.
The Third Question Family (Hurt Family) consists of only one question type—Weaken and it asks you to attack the author’s argument.
-
consists of one question type:
Weaken
-
Compared to the Second Question Family, the Help family, the only difference between the diagrams is that the third family diagram has a bar across the arrow. This bar signifies a negative: instead of strengthening or helping the argument, you attack or hurt the argument.
-
Rules:
- ## The information in the stimulus is suspect. There are often reasoning errors present, and you will further weaken the argument in some way.
- The answer choices are accepted as given, even if they include “new” information. Your task is to determine which answer choice best attacks the argument in the stimulus.
The ….. question family is based on the principle that you must use the information in the stimulus to prove that one of the answer choices cannot occur.
The Fourth Question Family (Hurt Family) consists of only one question type—Cannot Be True. As such, this question family is based on the principle that you must use the information in the stimulus to prove that one of the answer choices cannot occur.
-
consists of one question type:
Cannot Be True
-
The 4th question family is based on the principle that you must use the information in the stimulus to prove that one of the answer choices cannot occur. Compared to the First Question Family, the only difference in the diagram is that the Fourth Family diagram has a bar across the arrow. Again, this bar signifies a negative
-
Rules
- ## You must accept the stimulus information—even if it contains an error of reasoning—and use it to prove that one of the answer choices cannot occur.
- Any information in an answer choice that does not appear either directly in the stimulus or as a combination of items in the stimulus will be incorrect. The correct answer choice will directly disagree with the stimulus or a consequence of the stimulus.
How to approach stimulus of a Main Point Question
- Look for words that indicate Premises (since, because) and Conclusions (therefore, thus, hence, so, it follows that)
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- Look for words that indicate a Shift in Attitude (but, however)
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- Look for Evaluative Statements that indicate the author’s attitude
- Why Test
Quantity Indicators
Quantity Indicators
-
all
every
most
many
some
several
few
sole
only
not all
none
Probability Indicators
must
will
always
not always
probably
likely
should
would
not necessarily
could
rarely
never
Introduced by sufficient and necessary words such as: if…then, when, all, every, and only, where both elements are positive or both elements are negative
Introduced by conditional statements where exactly one of the terms is negative, or by statements using words such as “no” and “none” that imply the two variables cannot “go together.”
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Example Statement: No X’s are Y’s
Relationships involving Some
Row V Column
column is vertical
Columns are..
Vertical.
Think of roman columns
Rows are
Horizontal
Columns are Vertical
There are 4 people and each of them must drive at least once in the course of 6 days.
What is the greatest number of days each person can drive?
One person could drive three times with the other three driving once
3+1+1+1=6
-
The other possiblity is
Two people drive twice and two people drive once
2+2+1+1
Bob has a date with 7 girls on 5 days - Monday through Friday. Every girl gets a date and at least one date is scheduled each day.
What is the distribution
2 possibiltiies
3 on one day and 1 on the remaining 4
3 1 1 1 1 = 7
or
2 on two days and 1 on the remaining three
2 2 1 1 1 = 7
4 boys and 3 girls will be assigned to a row of 5 adjacent lockers.
Each locker must be assigned to either one or two children.
Each shared locker must be assigned to one boy and one girl.
What is the distribution
2 2 1 1 1
One girl will get her own locker
BG, BG, B, B, G
Most Vs The Most
Most - a majority = 50% +
The most can be a plurality = ie more than any other
reciprical?
Some is reciprical = create a line
most is not… its an arrow
A –all–> B
B — some–> C
Cant get anything from this
A –most–> B
B—most–> C
nothing
if it were Alls you could use the transative
A > B
B > C
A > C
All A’s are B’s
Some B’s are C’s
Nothing
Most A’s are B’s
Most A’s are C’s
Some B’s are C’s
Common Error/Flaw Type
1) Uncertain Use of a Term or Concept
2) Ad Hominem - flawed argument attacks the person (or source) instead of the argument they advance
3) Circular Reasoning - the author assumes as true what is supposed to be proved
4) Errors of Conditional Reasoning
5) Mistaken Cause and Effect (temporal relationship, correlation, alternate cause, reversal)
6) Straw Man - when an author attempts to attack an opponent’s position by ignoring the actual statements made by the opposing speaker and instead distorts and refashions the argument, making it weaker in the process
7) Lack of Relevant Evidence for the Conclusion
8) Internal Contradiction
9) Appeal Fallacies
a. Authority
b. Popular Opinion/Appeal to Numbers
c. Emotion
- Survey Errors
- Exceptional Case/Overgeneralization
- Errors of Composition and Division
- False Analogy
- False Dilemma
- Errors in the Use of Evidence
- Time Shift Errors
The Seperation Principle
Applies when variables involved in blocks/not-blocks are placed in a limited number of spaces resulting in the rigid allocation of the variables that can be exploited. EX: Rule: B__B__B and only 5 spaces available…so it would be, B1, B3, B5
Overlap Principle
When members of two separate variable sets are both assigned into a fixed number of spaces, there will be an overlap between the groups IF the sum of the two groups is greater than the total number of spaces. EX: There are three chairs in a classroom. Two of the chairs are green and two boys sit in the chairs. SO–Two variable sets are green chairs and boys…SUM of these two groups is 4, TOTAL number of spaces is 3 chairs…MEANS–at least 1 boy will sit in 1 green chair.
Either A is painted and B is painted, or A is not painted and B is not painted
J is painted if and only if K is not painted
J (double arrow) ~K
J is painted if and only if K is not painted
J (double arrow) ~K
What is implied by this statement
F –> G~
and
~G –> F
Which?
A) If Fran joins the team, Greg will not join tthe team
B) Fran will not join the team only if Greg does not join
C) Greg will not join the team if Frans joins the team, and Frans will join if Greg does not
C
F –> ~G
and
~G –> F
C) Greg will not join the team if Frans joins the team, and Frans will join if Greg does not
If Q is on the stage, then R is on the stage
R is not on the stage unless P is not on the stage
Q > R
R> ~P
P is negated and Necessary, – Double not arrow
R<–II–>P
Q<–II–>P
Diagram
If A is not interviewed then B must be interviewed, and
M –> O
One of them must be hired since there is only one space in the out group.
The original statement signifies that it is possible for one (M) not to be hired; however, if O isnt hired, M isnt hired, which would violate the game’s setup.
O must always be hired
If you are not T, then you are not V (T and V both negative)’
You can, of course take the contrapositive of this diagram and force both terms to be positive:
Some W’s are not Z’s
Some W’s are not Z’s
same as
Not all W’s are Z’s
“Some are not” can be defined as at least one is not, possibly all are
not. Thus, if I say, “Some of my friends are not present,” it could be true that none of my friends are present.
One of the most popular ways to introduce the idea that some are not is to use the phrase not all, which is functionally equivalent to some are not.
When diagramming statements involving some are not, simply place the word some between the two elements and negate the second element:
Not all T’s are V’s
Not all T’s are V’s – same as– Some T’s are not V’s
“Some are not” can be defined as at least one is not, possibly all are
not. Thus, if I say, “Some of my friends are not present,” it could be true that none of my friends are present.
One of the most popular ways to introduce the idea that some are not is to use the phrase not all, which is functionally equivalent to some are not.
When diagramming statements involving some are not, simply place the word some between the two elements and negate the second element:
Not all T’s are V’s – same as– Some T’s are not V’s
“Some are not” can be defined as at least one is not, possibly all are
not. Thus, if I say, “Some of my friends are not present,” it could be true that none of my friends are present.
One of the most popular ways to introduce the idea that some are not is to use the phrase not all, which is functionally equivalent to some are not.
When diagramming statements involving some are not, simply place the word some between the two elements and negate the second element:
Most X’s are Y’s
- most
- a majority
- more than half
- almost all
- usually
- typically
Most W’s are not Z’s
When “most” appears as “most are not,” the interpretation changes due to the not. “Most are not” can be defined as at majority are not, possibly all are not. Thus, if I say, “Most of my friends are not present,” it could be true that none of my friends are present.
When diagramming statements involving most are not, simply place the word most between the two elements, place an arrow under the most pointing at the second element, and negate the second element:
Most are not
When “most” appears as “most are not,” the interpretation changes due to the not. “Most are not” can be defined as at majority are not, possibly all are not. Thus, if I say, “Most of my friends are not present,” it could be true that none of my friends are present.
When diagramming statements involving most are not, simply place the word most between the two elements, place an arrow under the most pointing at the second element, and negate the second element:
Most W’s are not Z’s
Most W’s are not Z’s
When “most” appears as “most are not,” the interpretation changes due to the not. “Most are not” can be defined as at majority are not, possibly all are not. Thus, if I say, “Most of my friends are not present,” it could be true that none of my friends are present.
When diagramming statements involving most are not, simply place the word most between the two elements, place an arrow under the most pointing at the second element, and negate the second element:
