Flaw Flashcards
Error/Flaw Types
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
Ad Hominem
Source Argument Flaw - Also known as an ad hominem, this type of flawed argument attacks the person
(or source) instead of the argument they advance.
A source argument can take different forms, including the following:
- Focusing on the motives of the source.
- Focusing on the actions of the source (as in the below example).
“The anti-smoking views expressed by Senator Smith should be ignored. After all, Smith himself is a smoker!”
What is another name for a Source Argument Flaw
Ad Hominem
Source Argument Flaw - Also known as an ad hominem, this type of flawed argument attacks the person
(or source) instead of the argument they advance.
A source argument can take different forms, including the following:
- Focusing on the motives of the source.
- Focusing on the actions of the source (as in the below example).
“The anti-smoking views expressed by Senator Smith should be ignored. After all, Smith himself is a smoker!”
“it assumes what it seeks to establish”
Circular Reasoning
In circular reasoning the author assumes as true what is supposed to be proved
“presupposes the truth of what it sets out to prove”
Circular Reasoning
In circular reasoning the author assumes as true what is supposed to be proved
“it offers, in place of support for its conclusion, a mere restatement of
that conclusion”
Circular Reasoning
In circular reasoning the author assumes as true what is supposed to be proved
“it takes for granted the very claim that it sets out to establish”
Circular Reasoning
In circular reasoning the author assumes as true what is supposed to be proved
What is a synonym for Sufficient
in the same way that Required is a synonym for Necessary
Assured
It is interesting to note the frequency with which the words “sufficient” (or its
synonym “assured”) or “necessary” (or its synonym “required”) are used when
analyzing the answer choices used to describe conditional reasoning.
“taking the nonexistence of something as evidence that a necessary precondition for that thing also did not exist”
“taking the nonexistence of something as evidence that a necessary precondition for that thing also did not exist”
(Mistaken Negation)
“mistakes being sufficient to justify punishment for being required to justify it”
“mistakes being sufficient to justify punishment for being required to justify it”
(Mistaken Reversal)
Mistaken Cause and Effect
- Assuming a causal relationship on the basis of the sequence of events.
“mistakes the observation that one thing happens after another for proof that the second thing is the result of the first”
“mistakes a temporal relationship for a causal relationship” - Assuming a causal relationship when only a correlation exists.
“confusing the coincidence of two events with a causal relation between the two”
“assumes a causal relationship where only a correlation has been indicated” - Failure to consider an alternate cause for the effect, or an alternate cause for both the cause and the effect.
“fails to exclude an alternative explanation for the observed effect”
“overlooks the possibility that the same thing may causally contribute both to education and to good health” - Failure to consider that the events may be reversed.
“the author mistakes an effect for a cause”
If you identify a stimulus with causal reasoning and are asked a Flaw question, quickly…?
scan the answers for one that contains “cause” or “effect”
Straw Man
This error occurs 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. In figurative terms, a “straw” argument is built up which is then easier for the author to knock down.
“refutes a distorted version of an opposing position”
“misdescribing the student representative’s position, thereby making it easier to challenge”
“portrays opponents’ views as more extreme than they really are”
“distorts the proposal advocated by opponents”
Appeal to Authority
An Appeal to Authority uses the opinion of an authority in an attempt to persuade the reader. The flaw in this form of reasoning is that the authority may not have relevant knowledge or all the information regarding a situation, or there may a difference of opinion among experts as to what is true in the case
“the judgement of experts is applied to a matter in which their expertise is irrelevant”
“the argument inappropriately appeals to the authority of the mayor”
“it relies on the judgment of experts in a matter to which their expertise is irrelevant”
“accepts a claim on mere authority, without requiring sufficient justification”
Appeal to Popular Opinion/Appeal to Numbers
This error states that a position is true because the majority believes it to be true.
“A recent poll states that 75% of Americans believe that
Microsoft is a monopoly. Antitrust law states that monopolies have a deleterious effect on the marketplace (with the exception of utilities), and therefore Microsoft should be controlled or broken into smaller pieces.”
The author uses the results of a poll that indicate many people think Microsoft is a monopoly to conclude that Microsoft is in fact a monopoly
“it treats popular opinion as if it constituted conclusive evidence for a claim”
“attempts to discredit legislation by appealing to public
sentiment”
“a claim is inferred to be false merely because a majority of people believe it to be false”
“the argument, instead of providing adequate reasons in support of its conclusion, makes an appeal to popular opinion”
Appeal to Emotion
An Appeal to Emotion occurs when emotions or emotionally-charged language is used in an attempt to persuade the reader.
Here is an example:
“Officer, please do not give me a ticket for speeding. In the last month I’ve been fired from my job, kicked out of my apartment, and my car broke down. I don’t deserve this!
“attempts to persuade by making an emotional appeal”
“uses emotive language in labeling the proposals”
“the argument appeals to emotion rather than reason”
Survey Errors
The makers of the LSAT believe that surveys, when conducted properly, produce reliable results. However, surveys can be invalidated when either of the following three scenarios arise:
- The survey uses a biased sample.
- The survey questions are improperly constructed.
- Respondents to the survey give inaccurate responses
Exceptional Case/Overgeneralization
This error takes a small number of instances and treats those instances as if they support a broad, sweeping conclusion. Here is an example:
“Two of my friends were shortchanged at that store. Therefore, everyone gets shortchanged at that store. ”
This answer appears most frequently as an incorrect answer in Flaw questions, but as with any of the errors described in this chapter, occasionally it appears as
a correct answer.
“supports a universal claim on the basis of a single example”
“The argument generalizes from too small a sample of cases”
“Too general a conclusion is made about investing on the basis of a single experiment”
“bases a general claim on a few exceptional instances”
Errors of Composition and Division
Composition and division errors involve judgments made about groups and parts of a group.
An error of composition occurs when the author attributes a characteristic of part of the group to the group as a whole or to each member of the group
“Every party I attend is fun and exciting. Therefore, my life is fun and exciting.”
An error of division occurs when the author attributes a characteristic of the whole (or each member of the whole) to a part of the group. Here is an example:
“The United States is the wealthiest country in the world. Thus, every American is wealthy.”
Error of Composition
An error of composition occurs when the author attributes a characteristic of part of the group to the group as a whole or to each member of the group
“Every party I attend is fun and exciting. Therefore, my life is fun and exciting.”
Here are examples of how this error of reasoning is described in LSAT answer
choices:
“assuming that because something is true of each of the parts of a whole it is true of the whole itself”
“improperly infers that each and every scientist has a certain characteristic from the premise that most scientists have that characteristic”
“takes the view of one lawyer to represent the views of all lawyers”
Error of Division
An error of division occurs when the author attributes a characteristic of the whole (or each member of the whole) to a part of the group. Here is an example:
“The United States is the wealthiest country in the world. Thus, every American is wealthy.”
Here is an example of how this error of reasoning is described in LSAT answer choices:
“presumes, without providing justification, that what is true of a whole must also be true of its constituent parts”
when the author attributes a characteristic of the whole (or each member of the whole) to a part of the group.
An error of division occurs when the author attributes a characteristic of the whole (or each member of the whole) to a part of the group. Here is an example:
“The United States is the wealthiest country in the world. Thus, every American is wealthy.”
Here is an example of how this error of reasoning is described in LSAT answer choices:
“presumes, without providing justification, that what is true of a whole must also be true of its constituent parts”
when the author attributes a characteristic of part of the group to the group as a whole or to each member of the group
An error of composition occurs when the author attributes a characteristic of part of the group to the group as a whole or to each member of the group
“Every party I attend is fun and exciting. Therefore, my life is fun and exciting.”
Here are examples of how this error of reasoning is described in LSAT answer
choices:
“assuming that because something is true of each of the parts of a whole it is true of the whole itself”
“improperly infers that each and every scientist has a certain characteristic from the premise that most scientists have that characteristic”
“takes the view of one lawyer to represent the views of all lawyers”
Fallacy of Negative Proof
The author argues that since something has never been proven false, it must be true. Or, if something cannot be proven true, it must be false. This is a type of false consequences argument, since it assumes that all things must be proven true or false.
Negate ALL and SOME
ALL A are B. - negates to - SOME A are not B.
SOME A are B. - negates to - NO A are B.
or add All Not - All A are not B
Essentially, Some turns into No/None
Negate
ALL A are B
ALL A are B. - negates to - SOME A are not B.
SOME A are B. - negates to - NO A are B.
or add All Not - All A are not B
Essentially, Some turns into No/None
Negate
SOME A are B
SOME A are B. - negates to - NO A are B.
or add All Not - All A are not B
Essentially, Some turns into No/None
ALL A are B. - negates to - SOME A are not B.
Negate
“ALL students are opera singers.”
“SOME students are not opera singers.”
“ALL students are opera singers.”
Negate
“Some of the museum’s employees are not paid significantly more than minimum wage.”
It is not the case
(with rule - “Some” becomes “No/None)
“Some of the museum’s employees are not paid significantly more than minimum wage.”
original turns into: I V None of the museum's employees are not paid significantly more than the minimum wage. I V That leaves us with a double negative: none are not paid. We would translate this into I V "All of the museum's employees are paid significantly more than the minimum wage."
Negate
“All of the museum’s employees are paid significantly more than the minimum wage.”
“Some of the museum’s employees are not paid significantly more than minimum wage.”
SOME A are B. - negates to - NO A are B.
or add All Not - All A are not B
Essentially, Some turns into No/None
ALL A are B. - negates to - SOME A are not B.
Why does “ALL A are B” - negate to - “SOME A are not B”
Because “ALL A are B” means “every single one” negated becomes “NOT all/every single one”
Not all –> Some Are
Logical opposite of “None are”
Negation
Answer: “Some Are”
Some = 1 to 100 (everything but None) None = 0
Logical Opposites
All —— vs —— Not all/Some Not (Some or None)
Some —— vs —— None
All = 100
Not All = 0 to 99 (everything but All - could be Some or None –> hence SOME NOT)
Some = 1 to 100 (everything but None) None = 0
Logical Opposite
Negation
Logical Opposites
All —— vs —— Not all/Some Not (Some or None)
Some —— vs —— None
All = 100
Not All = 0 to 99 (everything but All - could be Some or None –> hence SOME NOT)
Some = 1 to 100 (everything but None) None = 0
Time
Always —— vs —— Not Always
Sometimes —— vs —— Never
Space
Everywhere —— vs —— Not Everywhere
Somewhere —— vs —— Nowhere
Negate
“ALL students are opera singers.”
“ALL students are opera singers.”
(Meaning that there are NO students who are not opera singers.)
negated becomes ->
“It is NOT true that ALL students are opera singers.”
»_space;» “SOME students are not opera singers.”
ALL A are B. negates to SOME A are not B.
Negate
“Some rectangles are squares.”
“Some rectangles are squares.”
(Meaning that there exists at least one rectangle that is a square. Possibly All)
negated becomes ->
“It is NOT true that some rectangles are squares.”
“NO rectangles are squares.”
SOME A are B. negates to NO A are B.
“ALL students are opera singers.”
“ALL students are opera singers.”
(Meaning that there are NO students who are not opera singers.)
negated becomes ->
“It is not true that ALL students are opera singers.”
“SOME students are not opera singers.”
How do you Negate a Conditional Statement
esp to check Assumption Question answers
To negate a conditional statement you must show that the necessary condition is not in fact necessary.
For example,
“To be rich, you must be smart” becomes
“To be rich, you do not necessarily have to be smart.”
A –> B
becomes
A –> ~B
Negate
The tax increase will result in more revenue for the government.
The tax increase will result in more revenue for the government.
becomes
The tax increase might not result in more revenue for the government.
The negation of “will” is “might not.” In practice the polar opposite “will not” tends to be acceptable
think all
Negate
“I will either sleep OR read”
The logical opposite of “I will either sleep OR read” is
“I will neither sleep nor read” (i.e. I will not sleep AND not eat).
Conversely, the logical opposite of “I will cook AND clean” is “I will not cook, OR will not clean.” (or not do either)
Negate
The tax increase will result in more revenue for the government.
The tax increase will result in more revenue for the government.
becomes
The negation of “will” is “might not.” In practice the polar opposite “will not” tends to be acceptable
think all
Negate
The councilmember could reverse her position
The councilmember could reverse her position
V
V
The councilmember cannot reverse her position.
“Cannot” is the opposite of “could.”
Negation of “could” is
Cannot
just like Some = None
Negate
The voting patterns in this precinct changed significantly in the past year
The voting patterns in this precinct changed significantly in the past year
negation
The voting patterns in this precinct did not change significantly in the past year
Negate
“I have some money.”
“I have some money.”
“No you don’t, you have none!”
I have NO money
Negate
The pattern of behavior in adolescents is not necessarily determined by the environment they are raised in.
The pattern of behavior in adolescents is not necessarily determined by the environment they are raised in.
becomes
The pattern of behavior in adolescents is necessarily determined by the environment they are raised in.
Negate
Organic farming methods promote crop resistance to pest attack.
Organic farming methods promote crop resistance to pest attack.
becomes
Organic farming methods do not promote crop resistance to pest attack.
Negate
All of the missions succeeded.
All of the missions succeeded.
becomes
Not all of the missions succeeded.
essentially 0-99%, at least some if not all did not succeed
Negate
If the policy is implemented, the education budget will be cut.
If the policy is implemented, the education budget will be cut.
becomes
If the policy is implemented, the education budget will not be cut.
Negate the necessary condition using “will not” or “might not.”
Negate
The positive effects of the U.S. immigration policy are everywhere.
The positive effects of the U.S. immigration policy are everywhere.
becomes
The positive effects of the U.S immigration policy are not everywhere.
Note that “positive” in this sentence does not become “negative.” To say “The negative effects of the U.S immigration policy are everywhere” would not negate the original.
They could be in 0-99% - think all –> Some not
Negate
If the policy is implemented, the education budget will be cut.
If the policy is implemented, the education budget will be cut.
becomes
If the policy is implemented, the education budget will not be cut.
Negate the necessary condition using “will not” or “might not.”
The positive effects of the U.S. immigration policy are everywhere.
becomes
The positive effects of the U.S immigration policy are not everywhere.
Note that “positive” in this sentence does not become “negative.” To say “The negative effects of the U.S immigration policy are everywhere” would not negate the original.
They could be in 0-99% - think all –> Some not
Negate
Unless the stock market rebounds, the economy will not recover this year.
Unless the stock market rebounds, the economy will not recover this year.
economy recover this year –> stock market rebounds
The economy will recover this year even if the stock market does not rebound.
REMEMBER to negate a conditional statement show that the Necessary Condition doesnt necessarily Need to occur
REMEMER to negate a conditional statement …
REMEMBER to negate a conditional statement show that the Necessary Condition doesnt necessarily Need to occur
Unless the stock market rebounds, the economy will not recover this year.
IF the economy recovesr this year –> THEN stock market Must rebound
VVV
The economy will recover this year even if the stock market does not rebound.
Negate
Exactly one police car will reach the scene in time.
Not exactly one police car will reach the scene in time.
Typically, there are two ways to negate a phrase containing the words “only one” or “exactly one.” One possibility is to use the term “none” and the other possibility is to use the phrase “more than once.”
Both are logical negations since you are attempting to negate a statement where something occurred a precise number of times. In this case, any statement that differs in number from the original statement will be a negation.
If this shows up in an assumption question, look for…
Premises: A –> B –> C
Conclusion: A –> D
C –> D
If conditional statements are linked together in the argument, the correct answer choice for an Assumption question will typically supply a missing link in the chain
On the LSAT, assumptions play one of two roles
Supporter Assumption: These assumptions link together new or rogue elements in the stimulus or fill logical gaps in the argument.
Defender Assumption: These assumptions contain statements that eliminate ideas or assertions that would
undermine the conclusion. In this sense, they “defend” the argument by showing that a possible avenue of attack has been eliminated (assumed not to exist).
- Logically negate the answer choices under consideration.
- The negated answer choice that attacks the argument will be the correct answer.
the correct answer to an Assumption question
will normally fit one of the following categories:
A. Eliminates any alternate cause for the stated effect
B. Shows that when the cause occurs, the effect occurs
C. Shows that when the cause does not occur, the effect does not occur
D. Eliminates the possibility that the stated relationship is reversed
E. Shows that the data used to make the causal statement are accurate, or eliminates possible problems with the data
On the LSAT, assumptions play one of two roles
Supporter Assumption: These assumptions link together new or rogue elements in the stimulus or fill logical gaps in the argument.
Defender Assumption: These assumptions contain statements that eliminate ideas or assertions that would
undermine the conclusion. In this sense, they “defend” the argument by showing that a possible avenue of attack has been eliminated (assumed not to exist).
the correct answer to an Assumption question
will normally fit one of the following categories:
A. Eliminates any alternate cause for the stated effect
B. Shows that when the cause occurs, the effect occurs
C. Shows that when the cause does not occur, the effect does not occur
D. Eliminates the possibility that the stated relationship is reversed
E. Shows that the data used to make the causal statement are accurate, or eliminates possible problems with the data
Easy way of making sure you got a logical negation correct
Add the phrase
“It is not the case”
Logical Opposite of
Some
Not one (None)
Logical Opposite of
None / Not One
Some
Logical Opposite of
Could
Cannot
Logical Opposite of
Cannot
Could
Logical Opposite of
Must be true
Not necessarily true
Logical Opposite of
Not necessarily true
Must be true
Negate
Some musicians are wealthy
No musicians are wealthy
Negate
P
Not P
Negate
It is Friday and it is raining
It is not Friday or it is not raining, or not both
negating turns and to or
Negate
It is Friday or it is raining
original statement - It is Friday or it is raining
F, R or both
Or turns into and
It is not Friday and it is not raining
Negate
If it is Friday, then it is raining.
It is Friday and it is not raining.
Cause and Effect - Assumption Question
A. Eliminates any alternate cause for the stated effect
B. Shows that when the cause occurs, the effect occurs
None of the museum’s employees are not paid significantly more than the minimum wage.
None of the museum's employees are not paid significantly more than the minimum wage. I V That's a double negative: none are not paid. We would translate this into I V "All of the museum's employees are paid significantly more than the minimum wage."
“Presuppose” is a synonym for
Assume
“The argument presupposes which of the following”
Is an assumption question
What do you do if you see “serves as an assumption” for a role question
Don’t select it
An assumption is an unstated premise. Therefore, it isn’t written in the argument
Negate
The president could veto the bill
The president cannot veto the bill
Negate
All of the teams played well
Not all of the teams played well
Some of the teams did not play well
Negate
If Smith gets elected, he will serve only one term as mayor
If smith gets elected he might not serve only one term as mayor
you can negate the necessary condition using “Wont necessarily” or “Might not”
Negate
The winner will not necessarily be determined during the first half of the game
The winner will be determined during the first half of the game
The detrimental effects of global warming can be felt everywhere
the detrimental effects of global warming cannot be felt everywhere - there are at least some areas where they arent felt
Negate
Early to bed and early to rise makes a person healthy, wealthy and wise
Early to bed and early to rise DOES NOT NECESSARILY make a person healthy, wealthy and wise
New methods of warfare led to increased causality rates
New methods of warfare DID NOT lead to increased causality rates
Justify this statement
Premise
This month there was an increase in the percentage of callers who made a purchase compared to last month
Conclusion
More callers made a purchase this month than made a purchase last month
The number of callers did not decrease from last month
This problem features numbers and percentages. The test makers could have used an answer that is roughly the same as “the rate of decrease did not exceed the rate of increase of purchase percentage,” but this is less likely to occur without some knowledge of the group
What are the 4 Errors in the Use of Evidence
- Lack of evidence for a position is taken to prove that position is false (Lack of E = True)
- Lack of evidence against a position is taken to prove that position is true (Lack of E = False)
- Some evidence against position taken to prove that position is false (Some E Against = False)
- Some evidence for a position is taken to prove that position is true (Some E For = True)
Evidence Contradicts Conclusion:
Evidence Contradicts Conclusion:
Very rare correct answer - common trap
Ex if right would be: “This book didn’t sell well at all; nearly all copies printed were returned to the publisher. It follows that the publisher should print more copies as soon as possible.”
If the book didn’t sell the logical inference is that more copies should NOT be printed.
This pattern is rare. The the evidence in any Assumption Family Question (Anything with assumption - Flaw, Strengthen, Weaken, Principle) will never fully prove the conclusion, it is almost never happens that the evidence actually contradicts the conclusion.
Exceptional Cases and Overgeneralizations
A stimulus with this flaw typically presents a small number of instances (maybe a single case, but never more than a few) and treats those instances as though they substantiate a broad, often sweeping, conclusion.
ex:
“My friend swears the mechanic at that shop overcharged her last week and after looking at her invoice it seems she’s right. So don’t take your business there, as you’ll definitely get ripped off.”
This is a very specific type of mistake and follows from a very consistent construction, so unless you see a generalized (broad) conclusion following a limited number of instances, do NOT pick an answer like those above. They are very commonly presented as traps following stimuli with other reasoning errors.
Reductio ad absurdum
Often used as a method of reasoning against a first perspective or speaker
Using a line of reasoning to draw an absurd conclusion
you take a statement which you wish to prove false, and show that if you assume it to be true, then it necessarily leads to a logical contradiction. Or to put it a bit more formally, If statement A is true, then statement B is true, and statement B is false. Therefore, statement A is not true. A ~B ------ A - B B + ~B .: ~A
Arguments which use universals such as, “always”, “never”, “everyone”, “nobody”, etc., are prone to being reduced to absurd conclusions. The fallacy is in the argument that could be reduced to absurdity – so in essence, reductio ad absurdum is a technique to expose the fallacy.
Assume P is true. From this assumption, deduce that Q is true. Also deduce that Q is false.
Thus, P implies both Q and not Q (a contradiction, which is necessarily false).
Therefore, P itself must be false.
Non Sequitur
Non sequitur (Latin for “it does not follow”),
in logic, it is an argument in which its conclusion does not follow from its premises.
In a non sequitur, the conclusion could be either true or false, but the argument is fallacious/unsound because there is a disconnection between the premise and the conclusion. All invalid arguments are special cases of non sequitur.
How to negate an AND statement
And becomes NEITHER - not either
Both table tennis and darts are playable underwater
Becomes
Neither table tennis nor darts is playable underwater
Not A or not B means
Not A or not B means
Not Both
Could be zero, one
How to negate an Or
A or B - at least one or both
Becomes
Not A or not B - means not both. Could be zero, could be one, can’t be two
Diagram
She will buy either a Jetski or a Boat, but not both
(J or B) + (~J or ~B)
At least one - Not both (negated or)
Diagram
Ralph cannot complete both the Bread and the Steak
~B or ~S
Not Bread, Not Steak, or Not Both
Zero, One, None, just not Both
How to Negate - conjunction and disjunctions
And Or
Negated AND (both) becomes neither, (not both) - Zero
Negated OR becomes at most one, possibly neither
What does this mean:
Not A or not B
Could be just A, just B, or neither (zero) - it just can’t be both
Negated OR
(A or B) + (~A or ~B)
Diagram and form contrapositive
The only way to make the baby stop crying is to give it some medication or whiskey but not both
Sc > (M or W) + (~M or ~W)
-
(~M + ~W) or (M + W) > ~SC
If the baby takes neither Medicine and whiskey, both medicine and whiskey, then it will not stop crying
Diagram
If it is not the case that the park contains both laurels and oaks, then it must contain firs and spruces
~L or ~O > F and S
Have to have both of one set
~F or ~S > L and O
If you are missing L or S then you must have both L and O
(~L or ~O)
Not L or not O
It translates to - Just L, just O, or neither, just not both
When it is mixed with L or O - at least one, possibly both, just not none \+ (L or O) It becomes (~L or ~O) + (L or O) - L or O, just not both
(L or O)
At least one of L or O, possibly both of them.
When Not L or not O (~L or ~O) one or the other, just not both is added, it becomes
(L or O) + (~L or ~O)
L or O, just not both (exactly one)
Y > (L or O) + (~L or ~O)
Contrapositive…
Y > (L or O) + (~L or ~O)
(~L and ~O) or (L and O) > ~Y
If neither L nor O, or both L and O, then no Y
(~L and ~O)
Neither L nor O
Negation of (L and O)
Y > (L or O) + (~L or ~O)
(~L and ~O) or (L and O) > ~Y
If neither L nor O, or both L and O, then no Y
(L and O)
Both L and O
Y > (L or O) + (~L or ~O)
(~L and ~O) or (L and O) > ~Y
If neither L nor O, or both L and O, then no Y
Diagram:
Neither L nor O
(~L and ~O)
Negation of L and O
Diagram:
Just L or just O or neither
(~L or ~O)
Y > (L or O) + (~L or ~O)
(~L and ~O) or (L and O) > ~Y
If neither L nor O, or both L and O, then no Y
