GMAT CR CONDITIONAL LOGIC — COMPLETE MASTER SHEET This sheet is designed for: Must Be True questions Assumption questions Strengthen/Weaken questions Formal logic CR Difficult inference questions The goal is: convert English into logical relationships without overload. PART 1 — THE CORE IDEA An arrow: A → B means: “If A happens, B must be true.” OR: “Every A is a B.” Example 1 Meaning: dog → mammal Interpretation: If something is a dog, it must be a mammal. Example 2 Meaning: rose → flower Interpretation: If something is a rose, it must be a flower. PART 2 — HOW TO TRANSLATE SENTENCES Do NOT focus on grammar first. Use this process: STEP 1 Ask: “Who or what are we talking about?” That usually becomes the LEFT side. STEP 2 Ask: “What must be true about them?” That becomes the RIGHT side. Example Question 1: Who are we talking about? Answer: teachers Question 2: What must be true about teachers? Answer: they are certified So: teacher → certified PART 3 — “ALL” STATEMENTS Structure Translation: A → B Example 1 Translation: bird → feathers Meaning: If something is a bird, it has feathers. Example 2 Translation: employee → badge Meaning: If someone is an employee, they wear a badge. IMPORTANT This does NOT mean: badge → employee Because visitors may also wear badges. PART 4 — THE REVERSE TRAP This is the MOST IMPORTANT trap in conditional logic. If: doctor → licensed DO NOT reverse it into: licensed → doctor Wrong. Why? Because: nurses may be licensed lawyers may be licensed many licensed people are not doctors GMAT LOVES THIS TRAP Example Passage: Wrong conclusion: Wrong because: scientist → educated does NOT mean: educated → scientist PART 5 — CONTRAPOSITIVE This is the ONLY valid flip. If: A → B Then: not B → not A This is ALWAYS logically valid. Example 1 doctor → licensed Contrapositive: not licensed → not doctor Meaning: If someone is not licensed, they cannot be a doctor. Example 2 bird → feathers Contrapositive: no feathers → not bird Meaning: If something lacks feathers, it cannot be a bird. PART 6 — “ONLY” This confuses almost everyone initially. Structure Translation: A → B The word after “only” becomes REQUIRED. Example 1 Who are we talking about? People entering. What must be true? They are members. Translation: enter → member Example 2 Who are we talking about? People operating the machine. What must be true? They are trained staff. Translation: operate machine → trained staff IMPORTANT This does NOT mean: trained staff → operate machine Because trained staff may choose not to operate it. PART 7 — “ONLY IF” Treat it the SAME way as “only.” Example Who are we talking about? People graduating. What must be true? They completed the thesis. Translation: graduate → thesis completed PART 8 — “NO” STATEMENTS Structure Translation: A → not B OR equivalently: B → not A Because the two groups cannot overlap. Example 1 Translation: reptile → not warm-blooded Equivalent meaning: warm-blooded → not reptile Example 2 Meaning: If a street has a bike lane, buses do not travel there. Translation: bike lane → no buses Equivalent: buses present → no bike lane PART 9 — CHAINING If: A → B B → C Then: A → C Example Translation: one-way → bike lane bike lane → no buses Chain them: one-way → no buses PART 10 — USING CONTRAPOSITIVE ON CHAINS If: one-way → no buses Contrapositive: buses present → not one-way This is how many GMAT inference questions are solved. PART 11 — “SOME” This is VERY different from conditional logic. Structure Meaning ONLY: at least one overlap exists NOT: A → B Example Correct inference: At least one doctor is a researcher. WRONG inference: All doctors are researchers. WRONG inference: Most doctors are researchers. PART 12 — “MOST” Structure Meaning: more than half of A are B NOT: all almost all every Example Valid: More than half passed. Invalid: All students passed. PART 13 — “UNLESS” Easy translation rule: Structure unless X = if not X, then Y Example 1 Equivalent meaning: If you do NOT have a ticket, you cannot enter. Translation: no ticket → no entry Equivalent: enter → ticket Example 2 Translation: not watered → die Equivalent: survive → watered PART 14 — COMMON GMAT TRAPS Trap 1 — Reverse If: A → B Wrong: B → A Trap 2 — Negation Trap If: A → B Wrong: not A → not B Not valid. Example doctor → licensed WRONG: not doctor → not licensed Because nurses may be licensed. Trap 3 — Strength Jump Passage: some A are B Wrong answer: most A are B Trap 4 — Cause Injection Passage: A happened before B Wrong: A caused B Sequence does not prove causation. Trap 5 — Scope Expansion Passage about: some cities Wrong answer about: all countries PART 15 — FAST MBT SOLVING METHOD Step 1 Translate important relationships into arrows. Step 2 Chain relationships if possible. Step 3 Use contrapositives carefully. Step 4 Attack answer choices by asking: “Could this still be false?” If YES: eliminate. PART 16 — THE ENTIRE CONDITIONAL TOOLKIT English Structure Translation All A are B A → B Every A is B A → B Any A is B A → B Only B can do A A → B A only if B A → B No A are B A → not B Some A are B overlap exists Most A are B more than half A unless B not B → A FINAL SIMPLIFICATION For GMAT CR, conditional logic is mostly: Translate relationships correctly Avoid reversing arrows Use contrapositives Chain relationships Stay disciplined about certainty You do NOT need complicated formal logic notation beyond this for almost all GMAT CR questions.

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Conditionals in CR and DI

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GMAT CR CONDITIONAL LOGIC — COMPLETE MASTER SHEET
This sheet is designed for:

Must Be True questions
Assumption questions
Strengthen/Weaken questions
Formal logic CR
Difficult inference questions

The goal is:
convert English into logical relationships without overload.

PART 1 — THE CORE IDEA
An arrow:

Code:

A → B

means:
“If A happens, B must be true.”
OR:
“Every A is a B.”

Example 1

Quote:

All dogs are mammals.

Meaning:

Code:

dog → mammal

Interpretation:
If something is a dog, it must be a mammal.

Example 2

Quote:

All roses are flowers.

Meaning:

Code:

rose → flower

Interpretation:
If something is a rose, it must be a flower.

PART 2 — HOW TO TRANSLATE SENTENCES
Do NOT focus on grammar first.
Use this process:

STEP 1
Ask:
“Who or what are we talking about?”
That usually becomes the LEFT side.

STEP 2
Ask:
“What must be true about them?”
That becomes the RIGHT side.

Example

Quote:

All teachers are certified.

Question 1:
Who are we talking about?
Answer:
teachers
Question 2:
What must be true about teachers?
Answer:
they are certified
So:

Code:

teacher → certified

PART 3 — “ALL” STATEMENTS

Structure

Quote:

All A are B

Translation:

Code:

A → B

Example 1

Quote:

All birds have feathers.

Translation:

Code:

bird → feathers

Meaning:
If something is a bird, it has feathers.

Example 2

Quote:

All employees wear badges.

Translation:

Code:

employee → badge

Meaning:
If someone is an employee, they wear a badge.

IMPORTANT
This does NOT mean:

Code:

badge → employee

Because visitors may also wear badges.

PART 4 — THE REVERSE TRAP
This is the MOST IMPORTANT trap in conditional logic.

If:

Code:

doctor → licensed

DO NOT reverse it into:

Code:

licensed → doctor

Wrong.
Why?
Because:

nurses may be licensed
lawyers may be licensed
many licensed people are not doctors

GMAT LOVES THIS TRAP

Example
Passage:

Quote:

All scientists are educated.

Wrong conclusion:

Quote:

All educated people are scientists.

Wrong because:

Code:

scientist → educated

does NOT mean:

Code:

educated → scientist

PART 5 — CONTRAPOSITIVE
This is the ONLY valid flip.

If:

Code:

A → B

Then:

Code:

not B → not A

This is ALWAYS logically valid.

Example 1

Code:

doctor → licensed

Contrapositive:

Code:

not licensed → not doctor

Meaning:
If someone is not licensed, they cannot be a doctor.

Example 2

Code:

bird → feathers

Contrapositive:

Code:

no feathers → not bird

Meaning:
If something lacks feathers, it cannot be a bird.

PART 6 — “ONLY”
This confuses almost everyone initially.

Structure

Quote:

Only B can do A

Translation:

Code:

A → B

The word after “only” becomes REQUIRED.

Example 1

Quote:

Only members may enter.

Who are we talking about?
People entering.
What must be true?
They are members.
Translation:

Code:

enter → member

Example 2

Quote:

Only trained staff can operate the machine.

Who are we talking about?
People operating the machine.
What must be true?
They are trained staff.
Translation:

Code:

operate machine → trained staff

IMPORTANT
This does NOT mean:

Code:

trained staff → operate machine

Because trained staff may choose not to operate it.

PART 7 — “ONLY IF”
Treat it the SAME way as “only.”

Example

Quote:

You may graduate only if you complete the thesis.

Who are we talking about?
People graduating.
What must be true?
They completed the thesis.
Translation:

Code:

graduate → thesis completed

PART 8 — “NO” STATEMENTS

Structure

Quote:

No A are B

Translation:

Code:

A → not B

OR equivalently:

Code:

B → not A

Because the two groups cannot overlap.

Example 1

Quote:

No reptiles are warm-blooded.

Translation:

Code:

reptile → not warm-blooded

Equivalent meaning:

Code:

warm-blooded → not reptile

Example 2

Quote:

No buses travel on streets with bike lanes.

Meaning:
If a street has a bike lane, buses do not travel there.
Translation:

Code:

bike lane → no buses

Equivalent:

Code:

buses present → no bike lane

PART 9 — CHAINING
If:

Code:

A → B
B → C

Then:

Code:

A → C

Example

Quote:

All one-way streets have bike lanes.
Streets with bike lanes do not allow buses.

Translation:

Code:

one-way → bike lane
bike lane → no buses

Chain them:

Code:

one-way → no buses

PART 10 — USING CONTRAPOSITIVE ON CHAINS
If:

Code:

one-way → no buses

Contrapositive:

Code:

buses present → not one-way

This is how many GMAT inference questions are solved.

PART 11 — “SOME”
This is VERY different from conditional logic.

Structure

Quote:

Some A are B

Meaning ONLY:

Code:

at least one overlap exists

NOT:

Code:

A → B

Example

Quote:

Some doctors are researchers.

Correct inference:
At least one doctor is a researcher.
WRONG inference:
All doctors are researchers.
WRONG inference:
Most doctors are researchers.

PART 12 — “MOST”

Structure

Quote:

Most A are B

Meaning:

Code:

more than half of A are B

NOT:

all
almost all
every

Example

Quote:

Most students passed the exam.

Valid:
More than half passed.
Invalid:
All students passed.

PART 13 — “UNLESS”
Easy translation rule:

Structure

Code:

unless X
=
if not X, then Y

Example 1

Quote:

You cannot enter unless you have a ticket.

Equivalent meaning:
If you do NOT have a ticket, you cannot enter.
Translation:

Code:

no ticket → no entry

Equivalent:

Code:

enter → ticket

Example 2

Quote:

Plants die unless watered regularly.

Translation:

Code:

not watered → die

Equivalent:

Code:

survive → watered

PART 14 — COMMON GMAT TRAPS

Trap 1 — Reverse
If:

Code:

A → B

Wrong:

Code:

B → A

Trap 2 — Negation Trap
If:

Code:

A → B

Wrong:

Code:

not A → not B

Not valid.

Example

Code:

doctor → licensed

WRONG:

Code:

not doctor → not licensed

Because nurses may be licensed.

Trap 3 — Strength Jump
Passage:

Code:

some A are B

Wrong answer:

Code:

most A are B

Trap 4 — Cause Injection
Passage:

Code:

A happened before B

Wrong:

Code:

A caused B

Sequence does not prove causation.

Trap 5 — Scope Expansion
Passage about:

Code:

some cities

Wrong answer about:

Code:

all countries

PART 15 — FAST MBT SOLVING METHOD

Step 1
Translate important relationships into arrows.

Step 2
Chain relationships if possible.

Step 3
Use contrapositives carefully.

Step 4
Attack answer choices by asking:
“Could this still be false?”
If YES:
eliminate.

PART 16 — THE ENTIRE CONDITIONAL TOOLKIT

English Structure	Translation
All A are B	A → B
Every A is B	A → B
Any A is B	A → B
Only B can do A	A → B
A only if B	A → B
No A are B	A → not B
Some A are B	overlap exists
Most A are B	more than half
A unless B	not B → A