Logic Reasoning

Question 1

If X, then Y

If Joan had gotten an A on her paper, she could pass the course without doing the presentation.

Answer 1

X → Y
not Y → not X

A on paper → can pass w/o pres.
can’t pass w/o pres. → not A on paper

Question 2

X if Y
People can feel secure if they are governed by laws that are not vague.

Answer 2

Y → X
not X → not Y

not vague laws → can feel secure
can’t feel secure → vague laws

Pay attention to the location of the word “if”! Wherever “if” appears within the sentence, it will be immediately followed by the trigger, regardless of whether “if” is at the beginning or in the middle of the sentence.

Question 3

X only if Y

Knowledge can be gained only if medical consent is sometimes bypassed.

Answer 3

X → Y
not Y → not X

knowledge can be gained → med. consent sometimes bypassed
med. consent never bypassed → knowledge can’t be gained

“Only if” is not the same thing as “if”. “Only if” indicates a necessary condition while “if” by itself indicates a sufficient condition. On Test Day, try simply changing “only if” into an arrow!

Question 4

Only X are Y

Only propositions that can be proven true can be known to be true.

Only those proposals the director supports will be approved.

Answer 4

Y → X
not X → not Y

can be known to be true → can be proven true
can’t be proven true → can’t be known to be true

“Only” indicates a necessary condition, not a sufficient condition.

approved → director support
[Some proposals the director supports will not be approved]
[Director support doesn’t guarantee approval]

Question 5

Any X is/are Y
Any moon, by definition, orbits a planet.

Answer 5

X → Y
not Y → not X

moon → orbits planet
not orbit planet → not moon

Question 6

Every X is Y

Every student who walks to school goes home for lunch.

Answer 6

X → Y
not Y → not X

walk to school → goes home for lunch
not go home for lunch→ not walk to school

Question 7

No X is/are Y

No strictly physical theory can explain consciousness.

Answer 7

X → not Y
Y → not X

strictly physical theory → can’t explain consciousness
can explain consciousness → not strictly physical theory

Diagram meanings; don’t diagram the statements word by word. “No X is Y” doesn’t mean “not X → Y”. Instead, it means that everything that is X, isn’t Y.

Question 8

X cannot be Y

Fitness consultants who smoke cigarettes cannot help their clients become healthier.

Answer 8

X → not Y
Y → not X

smoke cigarettes → can’t help clients get healthier
can help clients get healthier → don’t smoke cigarettes

Question 9

Without X there can be no Y

Without self-understanding it is impossible to understand others.

Answer 9

7SAGE says:
* no self understanding → impossible to understand others
* possible to understand others → self understanding

Group 3: You pick either idea, then negate that idea, then make that idea the sufficient condition. → this makes more sense to me

KHAN says:
Y → X
not X → not Y

understand others → self-understanding
not self-understanding → not understand others

This is basically saying that X is necessary for Y to be true. So, if you don’t have X, you can’t have Y.

Question 10

X requires Y

Novelists require some impartiality to get an intuitive grasp of the motions of everyday life.

Answer 10

X → Y
not Y → not X

The goal is the sufficient condition (on the left), while the requirement is to the right of the arrow. That’s because if a goal is met, then you can be certain that the requirement for the goal must also have been met.

intuitive grasp → impartiality
partiality → no intuitive grasp

Question 11

In order for X to be true, Y must be true

In order to understand Stuart’s art, Robbins must be able to pass judgment on it.

Answer 11

X → Y
not Y → not X

The goal is the sufficient condition (on the left), while the requirement is to the right of the arrow. That’s because if a goal is met, then you can be certain that the requirement for the goal must also have been met.

understand S’s art → able to pass judgment
not able to pass judgment → not understand S’s art

Question 12

X depends on Y

The existence of a moral order depends upon human souls being immortal.

Answer 12

X → Y
not Y → not X

moral order → human souls immortal
human souls not immortal → no moral order

What is “depended on” is the necessary condition. We depend on air to survive, so air is necessary. “X depends on Y” means that Y is necessary (not sufficient).

Question 13

X happens whenever Y happens

Inflation occurs whenever the money supply grows more than the production of goods and services grows.

Answer 13

Y → X
not X → not Y

money supply grows more than production grows → inflation
no inflation → money supply didn’t grow more than production grew

What event follows the other? Every time Y happens, X happens. That means that Y is the trigger for X condition to happen 100% of the time that Y happens.

Question 14

No X unless Y

Ann would not quit unless she were offered a fellowship.

Answer 14

7SAGE says:
* quit → offered internship
* not offered internship → not quit

Group 3: You pick either idea, then negate that idea, then make that idea the sufficient condition.

KHAN says:

X → Y
not Y → not X

Ann quits → Ann was offered fellowship
Ann not offered fellowship → Ann doesn’t quit

“Unless” doesn’t indicate a trigger! It always indicates a necessary condition. “I can’t go to the beach unless I find my sunscreen”: if I find my sunscreen, that doesn’t actually mean anything; I could still just stay home. But I need to find my sunscreen in order to even have a shot at going to the beach. So:
beach → sunscreen
no sunscreen → no beach

Question 15

Only if a sentence can be diagrammed is it grammatical.
Any grammatical sentence is recognized as grammatical by speakers of its language.

Speaker X’s sentence can be diagrammed. So, speaker X’s sentence will be recognized as grammatical by speakers of its language.

The linguist’s reasoning is flawed because it fails to consider the possiblity that

https://www.khanacademy.org/prep/lsat/task/6116664795512832/question/6

Answer 15

grammatical → can be diagrammed
grammatical → recognized as grammatical by speakers of its language

grammatical → can be diagrammed => this is a necessary condition to be grammatical

The support says that all grammatical sentences can be diagrammed.
But the support doesn’t say that all diagrammable sentences are grammatical. Just because a sentence must be diagrammable in order to be considered grammatical, doesn’t mean that it is necessarily grammatical just because it can be diagrammed.

Question 16

The only X are Y

The only kids with messy hair are the kids with brown eyes.

Answer 16

“The only” introduces sufficient conditions.
“Only” introduces a necessary condition.

The first grammatically correct usage:
The only X’s (insert modifiers) are the Y’s (insert modifiers).
In this form, the Y’s must call back, point back, refer back to the X’s.

The translation is X → Y.

For example:
The only kids with messy hair are the kids with brown eyes.
The only kids (X) with messy hair (modifier) are the kids (Y) with brown eyes (modifier).
Notice that Y refers back to X. You could have just as easily said:
The only kids with messy hair are the ones with brown eyes.
Translated: If you’re a kid with messy hair, then you have brown eyes. If you don’t have brown eyes, you don’t have messy hair.

Question 17

Y are the only X

Maniacal and over the top performances are the only effective ones.

Answer 17

“The only” introduces sufficient conditions.
“Only” introduces a necessary condition.

The second grammatically correct usage:
Y’s (insert modifier) are the only X’s (insert modifier).
In this form, the X’s must call back, point back, refer back to the Y’s.

The translation is X → Y.

One more example:
Maniacal and over the top performances are the only effective ones.
Maniacal and over the top (modifier) performances (Y) are the only effective (modifier) ones (X).
Notice the modifiers appear first.
Translated: If it’s an effective performance, then it was maniacal and over the top. If it was not maniacal or not over the top, then it was not effective.