LSAT Conditional Logic and Quantifiers: The Full Guide

With Logic Games gone, formal logic matters less on the LSAT than it once did, and prep has understandably shifted with the test. However, that has also made it easier to underprepare for the question types where conditional logic still shows up: Inference, Principle, Sufficient Assumption, Parallel Reasoning, and others.

That creates an opportunity for students to gain a competitive advantage by familiarizing themselves with the test’s logic. Learn the rules, practice the translations, and you’ll find that improvement here is much more consistent than in many other areas of the LSAT. What follows is a quick reference guide to help you with that practice.

Part 1: Conditional relationships

Identify the sufficient and necessary conditions first. Then translate the relationship into a diagram or plain English.

Conditional and "all" statements

A conditional is a relationship in which one condition guarantees another. Write it A guarantees B and read it as "if A, then B."

A is sufficient: if A occurs, B follows.
B is necessary: B is required for A.
One direction only: A guarantees B, but B does not guarantee A.

A map of France with Paris marked by a filled dot inside the country. — You are in Paris. If you are in Paris, then you are in France. Therefore, you are in France. `Paris guarantees France`

The contrapositive

For A guarantees B, the absence of B guarantees the absence of A. Two steps get you there:

Reverse — place the conditions in the opposite order.
Negate — negate both conditions.

So A guarantees B becomes ~not B guarantees ~not A. The contrapositive has the same meaning as the original conditional relationship.

A map of France with the marker placed outside the country, in the Atlantic, and Paris drawn as an empty circle. — You are not in France. If you are not in France, then you are not in Paris. Therefore, you are not in Paris. `~not France guarantees ~not Paris`

Part 2: Indicators

Which condition does the indicator introduce?

Sufficient condition indicators

The arrow points away from the term being modified by the indicator.

Invariably / Inevitably / Ensures / Guarantees / Is
A guarantees B
A valid ticket ensures entry.Ticket guarantees Entry
Will enable [someone] to / Allows
Condition guarantees Outcome
A key allows you to open the door.Key guarantees Can Open Door
All / Every / Any / When(ever) / Provided that / As long as
A guarantees B
Any valid contract is binding.Valid Contract guarantees Binding

Necessary condition indicators

The arrow points toward the subject of the indicator.

Can be explained only by
Phenomenon guarantees Cause
A crash can be explained only by pilot error.Crash Happened guarantees Pilot Error
Only / Only if / Only by / Only through
A guarantees B
The car starts only if there is gas.Starts guarantees Gas
Requires / Must / Essential / Presupposes / Precondition
A guarantees B
Evolution requires time.Evolution guarantees Time
Depends on / Is contingent on / Is governed by
A guarantees B
Survival depends on adaptation.Survive guarantees Adapt
Impossible without / In the absence of / But for
Result guarantees Requirement
Victory is impossible without sacrifice.Victory guarantees Sacrifice

Part 3: Quantifiers

How much of one group overlaps another?

All

12 of 12
Most

9 of 12, over half
Some

2 of 12, at least one
None

0 of 12
Few

3 of 12, under half

Filled circles show how many members also belong to the second group.

"Most" (more than 50%). More than half of the members of one group are in another group. "Most basketball players are tall" is Basketball Players most most are Tall People and tells you that over half of basketball players are tall.
"Some" (at least one). At least one member of a group is in another group. "Some basketball players are short" is Basketball Players some some are Short People and tells you at least one basketball player is short.
Many is a vague quantity. Treat it as some.
Few establishes two relationships at once. "Few politicians are independent" gives you both Politician some some are Independent and Politician most most are ~not Independent.

Hierarchy (all > most > some). A stronger quantifier can also imply a weaker one. For example, "All dogs are mammals" also tells you that some dogs are mammals.

Quantifier indicators

Some / Many / Several / Often / At least one
Some
Many birds migrate.Birds some some are Migrate
Most / Majority / Usually / Typically / Almost all
Most
Most businesses fail.Businesses most most are Fail
Few / Rarely / Seldom
Most of A are not B
Few people live to 100.People most most are ~not Live to 100
Not all / Not every
A some some are ~not B
Not all that glitters is gold.Glitters some some are ~not Gold
No / None
A guarantees ~not B
No square is a circle.Square guarantees ~not Circle

Part 4: Valid conclusions

The rule: an "all" conditional carries forward whatever quantifier reaches it.

All-to-all chain

All poodles are dogs, and all dogs are mammals. Every poodle therefore belongs to the larger group of mammals.

Poodle guarantees DogPremise
Dog guarantees MammalPremise
Poodle guarantees MammalConclusion

Most followed by all

Over 50% of US citizens live in the continental U.S., and everyone in the continental U.S. lives in North America. So over 50% of US citizens live in North America.

US Citizens most most are Continental USPremise
Continental US guarantees North AmericaPremise
US Citizens most most are North AmericaConclusion

Some-to-all chain

Some sea creatures are predators. Since every predator consumes other animals, those same sea creatures must consume other animals.

Sea Creatures some some are PredatorsPremise
Predators guarantees Consume Other AnimalsPremise
Sea Creatures some some are Consume Other AnimalsConclusion

Two majorities within one group

Eight of the twelve students study biology and seven study Spanish: fifteen enrollments among twelve students. Since each group is more than half the class, at least one student must study both. In this case, three do.

Students most most are Study BiologyPremise
Students most most are Study SpanishPremise
Study Biology some some are Study SpanishConclusion

No valid conclusion

Be very careful in dealing with a mixture of "all" and "some" conditionals, as you can see in this example. Even though every single person born in Alabama may be American, a strong relationship, and some Americans are born in Nebraska, it is clearly the case that no one (not some) born in Alabama is born in Nebraska. And so you can never confidently conclude anything from an "all" into "some" relationship.

A map of the United States with Alabama shaded solid and Nebraska shaded with diagonal stripes, two states that do not touch.

Part 5: Compound statements

And / Both
A + B
He is rich and famous.Rich + Famous
Or / Either … or
A or B
We can walk or drive.Walk or Drive
Neither … nor
~not A + ~not B
Neither rain nor snow stops the mail.~not Rain + ~not Snow

"And" and "or" inside a conditional

"And" in the necessary condition — A guarantees (B and C)
Splits into two relationships: A guarantees B and A guarantees C.
"And" in the sufficient condition — (A and B) guarantees C
Both sufficient conditions are required together. Do not split.
"Or" in the necessary condition — A guarantees (B or C)
At least one of the necessary conditions is required. Do not split.
"Or" in the sufficient condition — (A or B) guarantees C
Splits into two relationships: A guarantees C and B guarantees C.

Minimums, maximums, and nested conditions

At least one (minimum of one)
"You must choose A or B." Refuse one and you must take the other.
~not A guarantees B~not B guarantees A
Not both (maximum of one)
"You cannot choose both A and B." Take one and the other is out.
A guarantees ~not BB guarantees ~not A
Nested conditional
"If A happens, then if B happens, C happens." Read it as an "and" sufficient condition.
(A and B) guarantees C

Part 6: Negation

Negating a statement means identifying its exact logical opposite.

Negating "and" and "or": De Morgan's laws

When you take the contrapositive of a statement containing "and" or "or," change "and" to "or" and "or" to "and."

Original

A guarantees (B and C)

If you get promoted, you get a raise and an office.

Contrapositive

(~not B or ~not C) guarantees ~not A

If you don't get a raise or you don't get an office, you aren't promoted.

Original

(A or B) guarantees C

If it rains or snows, we stay inside.

Contrapositive

~not C guarantees (~not A and ~not B)

If we don't stay inside, it isn't raining and it isn't snowing.

Negating a quantifier

All
"All A are B" A guarantees B negates to "some A are not B" A some some are ~not B.
Most
"Most A are B" (over 50%) negates to "half or less" (0–50%).
Some
"Some A are B" (at least one) negates to "none" A guarantees ~not B.

Part 7: Exclusion, and the "unless" family

To translate a statement using "unless," identify the idea that follows "unless," negate that idea, and make the negated form sufficient. The other part of the sentence goes on the necessary side of the arrow.

Start with the sentence [B] unless [A] — "I will go to the movie unless it rains."
Negate [A] and make it sufficient "If it does not rain, then I will go to the movie."
Convert to a diagram ~not Rains guarantees Go

Use the same method for "except", "without", "until", and "or else".

Unless / Except / Without / Until / Or else
~not A guarantees B
The alarm rings unless the code is entered.~not Code guarantees Alarm
No / None / Never / Fail to be
A guarantees ~not B
No mammal breathes water.Mammal guarantees ~not Breathes Water
No [X] is both [Y] and [Z]
X guarantees ~not (Y + Z)
No number is both even and odd.Number guarantees ~not (Even + Odd)
Unless [A] or [B]
~not Trigger guarantees (A or B)
The deal fails unless you pay cash or trade goods.Deal Succeeds guarantees (Pay or Trade)
Not [A], let alone [B]
~not A + ~not B
He is not a mayor, let alone a president.~not Mayor + ~not President
No one who is not [A] is [B]
B guarantees A
No one who is not a lawyer is a judge.Judge guarantees Lawyer

Part 8: Two-way and hypothetical statements

Biconditionals

A biconditional is a two-way conditional relationship in which both A guarantees B and B guarantees A are true. Having either A or B guarantees the other.

If and only if / Then, and only then / All and only / When and only when
A if and only if B
A number is even if and only if it is divisible by two.Even if and only if Divisible by 2
Equivalent to / Is the same as saying / Exactly when
A if and only if B
Having exactly 100 cents is the same as having one dollar.100 Cents if and only if One Dollar

Hypotheticals and complex statements

Otherwise
~not A guarantees B
Wear a helmet, otherwise you risk injury.~not Helmet guarantees Risk Injury
Had [A] occurred, [B] would have occurred
A guarantees B
Had the levee held, the city would have remained dry.Levee Held guarantees Dry
[B] would not have occurred had [A] not occurred
~not A guarantees ~not B
The fire would not have started had the match not been struck.~not Match Struck guarantees ~not Fire Started
To [verb] / In order to
Goal guarantees Requirement
In order to make an omelet, you must break eggs.Omelet guarantees Break Eggs

Part 9: Cause and obligation

These relationships can resemble conditional statements, but they describe causation, obligation, permission, or judgment rather than a guaranteed result.

Causal indicators

Promotes / Leads to
Cause cause causes Effect
Exercise promotes health.Exercise cause causes Health
As a result
Cause cause causes Effect
The dam broke; as a result, the valley flooded.Dam Broke cause causes Flooded

Value judgments, obligations, and rights

Should / Ought to / Is obliged to
Condition guarantees Obligation
Citizens are obliged to pay taxes.Citizen guarantees Duty to Pay
Justified in
Condition guarantees Permissible
A person is justified in acting in self-defense if attacked.Attacked guarantees Self-Defense Permissible
Permissible only if
Permissible guarantees Condition
Entry is permissible only if you have a badge.Entry Permitted guarantees Badge
Unethical / Wrong / Should not [action] except [exception]
~not Exception guarantees ~not Action
Drivers shouldn't park here except when permitted.~not Permitted guarantees ~not Park

Part 10: Probability and belief

A is likely / probably / we would expect B
A most most are B
If you speed, you will likely get a ticket.Speed most most are Ticket
A tends to B
A most most are B
Power tends to corrupt.Power most most are Corrupt
A is unlikely unless B
A most most are B
Success is unlikely unless you plan.Success most most are Plan
Can thus rule out
A guarantees ~not B
The alibi rules out the suspect.Alibi guarantees ~not Suspect
[Person] says [A], so they believe [B]
Say(A) guarantees Believe(B)
He says the bank is open, so he believes he can deposit checks.Says(Open) guarantees Believes(Deposit)

Part 11: Conditional errors

These errors take a narrow premise and read a broader relationship into it than the evidence supports.

Illegal reversal and illegal negation

Illegal reversal. "If A, then B" does not tell you "if B, then A."
Illegal negation. "If A, then B" does not tell you "if not A, then not B."

Squares sit inside rectangles: every square is a rectangle, but most rectangles are not squares.

Square guarantees RectangleFollows
Rectangle guarantees SquareDoes not follow
~not Square guarantees ~not RectangleDoes not follow
~not Rectangle guarantees ~not SquareFollows

The "most" error

You are not allowed to end a conditional chain in a "most" and draw a conclusion.

NBA Players guarantees Tall PeoplePremise
Tall People most most are Non-AthletesPremise
NBA Players some some are Non-AthletesDoes not follow

All of the NBA players could be among the tall people who are athletes. Nothing requires even one NBA player to be a non-athlete.

That is different from a most-most. In Two Majorities Within One Group the two majorities come from the same group rather than from a chain, so they have to overlap.

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The Conditional Logic and Quantifier Guide