Foundations Flashcards
If
Group 1
When
Group 1
Where
Group 1
All
Group 1
Every
Group 1
Any
Group 1
The only
Group 1
Only
Group 2
Only if
Group 2
Only when
Group 2
Only where
Group 2
Always
Group 2
Must
Group 2
Or
Group 3
Unless
Group 3
Until
Group 3
Without
Group 3
No
Group 4
None
Group 4
Not both
Group 4
Cannot
Group 4
- If
- When
- Where
- All
- Every
- Any
- The only
Group 1 Indicators
Group 1 Indicators (7)
- If
- When
- Where
- All
- Every
- Any
- The only
The idea introduced by the indicator is the sufficient condition
Group 1
Group 1
The idea introduced by the indicator is the sufficient condition
Group 1 Ex. When zombies attack New York City, the real estate market will crash.
What is the sufficient condition?
zombies
Convert to lawgic: When zombies attack New York City, the real estate market will crash.
Z –> REC
/REC –> /Z
If the real estate market doesn’t crash, zombies are not attacking New York City.
- Only
- Only if
- Only when
- Only where
- Always
- Must
Group 2 Indicators
Group 2 Indicators (6)
- Only
- Only if
- Only when
- Only where
- Always
- Must
Group 2
The idea introduced by the indicator is the necessary condition
The idea introduced by the indicator is the necessary condition
Group 2
Group 2 Ex. Students are cited as “late” only if they arrive more than five minutes past the last ring of the homeroom bell.
What is the necessary condition?
arriving more than 5 minutes after the bell
Convert to lawgic: Students are cited as “late” only if they arrive more than five minutes past the last ring of the homeroom bell.
late –> 5+
/5+ –> /late
If a student does not arrive more than five minutes past the last ring of the bell, then they are not cited as late
- Or
- Unless
- Until
- Without
Group 3 indicators
Group 3 Indicators (4)
- Or
- Unless
- Until
- Without
Group 3
pick either idea, negate that idea, then make that idea the sufficient condition
pick either idea, negate that idea, then make that idea the sufficient condition
Group 3
Convert to lawgic: Blackouts will occur unless the heat wave abates
/BO –> HWA
/HWA –> BO
- No
- None
- Not both
- Cannot
Group 4 indicators
Group 4 Indicators (4)
- No
- None
- Not both
- Cannot
Group 4
pick either idea, negate that idea, then make that idea the necessary condition
pick either idea, negate that idea, then make that idea the necessary condition
Group 4
Convert to lawgic: None of the Americans attended the dictator’s party
ADP –> /American
American –> /ADP
Translate into lawgic:
If Amidala convinces the Senate and the Jedi Knights accomplish their mission, then the Chancellor’s nefarious plan will fail.
If Amidala convinces the Senate = A
the Jedi Knights accomplish their mission = J
the Chancellor’s nefarious plan will fail = CF
A and J —> CF
A + J ≠ A –> CF
J —> CF
A and J have to happen together. A can’t independenty cause CF and J can’t independenty cause CF
Translate into lawgic:
If M is adopted, then N and O are adopted.
M —> N and O
M —> N and O DOES =
M —> N AND M —> O
If a conjunction occurs within the sufficient condition…
both elements together guarantee the necessary condition. Neither alone is independently sufficient.
If a conjunction occurs within the necessary condition…
two events are independently necessary when the sufficient condition is triggered.
Translate into lawgic:
If the Chancellor’s plan succeeds, then either Amidala failed or the Jedi Knights failed.
CS —> AF or JF
(at least one failed. could be both)
Translate into lawgic:
If N or O is not adopted, then M cannot be adopted.
/N or /O —> /M
If N is not adopted, then M cannot be adopted, independent of O.
If O is not adopted, then M cannot be adopted.
/N or /O —> /M =
/N —> /M and /O —> /M
If a disjunction occurs in a necessary condition…
then at least one (possibly both) must trigger when the sufficient triggers.
If a disjunction occurs in a sufficient condition…
then two conditions can independently trigger the necessary condition
NEGATING AND
Translate the contrapositive into lawgic:
If M is adopted, then N and O must be adopted.
M –> N and O
/N or /O –> /M
How do you translate the contrapositive of “and”
Switch “and” for “or” and negate each element
Translate the contrapositive into lawgic:
If neither N or O are adopted, then M cannot be adopted
/N or /O –> /M
//M –> /(/N or /O)
or
//M –> //N or //O
=
M –> N and O
How do you translate the contrapositive of “or”
Switch “or” for “and” and negate each element
Few
quantifier
several
quantifier
many
quantifier
some
quantifier
most
quantifier
Quantifiers (5)
- few
- several
- many
- some
- most
what does several mean
more than one
what does most mean
more than half
what does some mean
at least 1
Some students in Mrs. Stoops’ class can read.
what must be true in regards to some
at least one student can read
Some students in Mrs. Stoops’ class can read.
what must be false in regards to some
no student can read
Some students in Mrs. Stoops’ class can read.
what could be true in regards to some
two students can read
ten students can read
fifteen students can read
all twenty students can read
what is the lower boundary for “some”
“at least one”
what is the upper boundary for “some”
there is no upper boundary. it could include all of the members of the group in question
what could “some” exclude?
all
Though reading is a challenge for students this young, some students in Mrs. Stoops’ class can read.
Mark the following statements as almost certainly false, could be false, could be true, must be true, and must be false:
- Three students can read
- All 20 students can read
- Eight students can read
- No student can read
- At least one student can read
- could be true
- almost certainly false
- could be true
- must be false
- must be true
Translate into lawgic: Some students in Mrs. Stoops’ class can read
students <- s -> read
read <- s -> students
what is the lower bound of most?
half. most suggests more than half.
Most students in Mrs. Stoops’ class can read. What must be true, what must be false, and what could be true?
Must be true: at least 11 students can read
Must be false: 10 or fewer students can read
Could be true: 12 students, 15 students, or all students can read
What is the upper bound for most?
Most does not have an upper bound. it could include all. it’s implied to exclude all.
We will meet our environmental goals only if most cars become electric.
If all cars become electric, do you fail the condition?
no
“most” in lawgic
–m–>
how must “most” be read
unidirectionally. it can’t be read reversibly.
how must “some” be read
bi-directional
Translate into Lawgic:
Most students in Mrs. Stoops’ class can read.
student –m–> read
why is read –m–> student a wrong translation of “Most students in Mrs. Stoops’ class can read”?
it suggests most students that can read are in Mrs. Stoops’ class, which is not identical to student –m–> read
what is “most A are B” not identical to?
“most B are A.”
what are the lower and upper bounds for “all”
“all” doesn’t have a lower or upper bound
what does all mean?
all. literally all.
Translate into lawgic:
All students at Hogwarts School of Witchcraft and Wizardry have magical abilities.”
S –> M
what is the contrapositive of “some” claims
there is no contrapositive of “some”
what is the contrapositive of “most” claims
there is no contrapositive of “most” claims
A <–s–> B does not equal…
/A <–s–> /B
A –m–> B does not equal…
/B –m–> /A
A –> B does imply
/B –> /A
what is the lower bound of “overwhelming majority”
higher than most.
- overwhelming majority raises the floor up from most
“An overwhelming majority of legislators on the city counsel voted against the new proposal.”
Assign the following as must be false, must be true, and could be true
100% voted against
90% voted against
80% voted against
70% voted against
60% voted against
51% voted against
100% - could be true
90% - could be true
80% - could be true
70% - must be true (lower boundary)
60% - must be true (lower boundary)
51% - must be false
what does “many” indicate
a large amount
what is the lower boundary for “many”
the lower boundary must be higher than “some”
practically speaking, what can you equate “many” with on the LSAT, and what can you not equate it with?
on the LSAT, you can equate “many” to “some”
you can not equate “many” to “most”
why can you not equate “many” with “most”?
most = more than half
technically, many only implies some
what does “few” mean?
some, but not many
some are, and most are not
how else can you say “Few silent films have survived into the twenty-first century”
Some, but not many silent films have survived into the twenty-first century.
Most silent films have not survived into the twenty-first century.
translate into lawgic:
Few silent films have survived into the twenty-first century.
silent <–s–> survive
and
silent –m–> /survive
what does all imply?
most
what does “all dogs like bacon” imply?
most dogs like bacon
what does most imply?
some
what does “most cats are furry” imply?
some cats are furry
if “all” implies “most” and “most” implies “some,” then what must be true?
“all” implies “some”
what does “all A are B” negate to?
some A are not B
what does “A –> B” negate to?
A <–s–> /B
what does “All dogs are friendly” negate to?
It’s not the case that all dogs are friendly
OR
Some dogs are not friendly
what does “If A then B” negate to? (conditional)
A can occur and B not occur
what does “A –> B” negate to? (conditional)
A and /B
what does “To be a Jedi, one must be able to use the Force” negate to?
It’s not the case that to be a Jedi, one must be able to use the Force.
OR
One can be a Jedi and not be able to use the Force
OR
Being a Jedi does not require being able to use the Force
what is a trap negation for “To be a Jedi, one must be able to use the Force”
To be a Jedi, one must not be able to use the Force
what does J –> F negate to?
/(J –>F)
OR
J and /F
what does “some A are B” negate to?
No A are B
what does A <–s–> B negate to?
A –> /B
What does “some parrots are clever” negate to?
It’s not the case that some parrots are clever
OR
All parrots are not clever
P –> /C
what does “most A are B” negate to?
It’s not the case that most A are B
OR
Anywhere from none to exactly half of A are B
