LSAT Formal Logic and Conditional Reasoning

Helping train logical reasoning for the LSAT. For cards with terms such as “Confusing Sufficiency for Necessity (INVALID)”, aim to memorize the structure before flipping the card.

Confusing Sufficiency for Necessity (INVALID)

A → B
_________
B → A

A → B
_________
B → A

INVALID OR VALID?

INVALID (Confusing Sufficiency for Necessity)

Denying the Sufficient Condition (INVALID)

A → B
/A
_________
/B

A → B
/A
_________
/B

Invalid or Valid?

INVALID (Denying the Sufficient Condition)

Affirming the Necessary Condition (INVALID)

A → B
B
________
A

A → B
B
________
A

Invalid or Valid?

INVALID (Affirming the Necessary Condition)

Most Statements are NOT Reversible (INVALID)

A —m→ B
_________
B —m→ A

A —m→ B
_________
B —m→ A

Invalid or Valid?

INVALID (Most Statements are NOT Reversible)

All Before Most (INVALID)

A → B —m→ C
_________
A ←s→ C

A → B —m→ C
_________
A ←s→ C

Invalid or Valid?

INVALID (All Before Most)

All Before Some (INVALID)

A → B ←s→ C
_____________
A ←s→ C

A → B ←s→ C
_____________
A ←s→ C

Invalid or Valid?

INVALID (All Before Some)

Most Before Most (INVALID)

A —m→ B —m→ C
__________________
A ←s→ C

A —m→ B —m→ C
__________________
A ←s→ C

Invalid or Valid?

INVALID (Most before Most)

Some Before Some (INVALID)

A ←s→ B ←s→ C
______________
A ←s→ C

A ←s→ B ←s→ C
______________
A ←s→ C

Invalid or Valid?

INVALID (Some before Some)

The Conditional Argument (VALID)

 A → B
_(x)A
________
_(x)B

 A → B
_(x)A
________
_(x)B

Invalid or Valid?

VALID (Conditional Argument)

The Contrapositive Argument (VALID)

A → B
_(x)/B
________
_(x)/A

A → B
_(x)/B
________
_(x)/A

Invalid or Valid?

VALID (Contrapositive Argument)

Conditional Chaining (VALID)

A → B → C
________
A → C

A → B → C
________
A → C

Invalid or Valid?

VALID (Conditional Chaining)

Some Before All (VALID)

A ←s→ B → C
________
A ←s→ C

A ←s→ B → C
________
A ←s→ C

Invalid or Valid?

VALID (Some Before All)

Most Before All (VALID)

A —m→ B → C
________
A —m→ C

A —m→ B → C
________
A —m→ C

Invalid or Valid?

VALID (Most Before All)

Two Mosts (VALID)

A —m→ B
A —m→ C
________
B ←s→ C

A —m→ B
A —m→ C
________
B ←s→ C

Invalid or Valid?

VALID (Two Mosts)

Translate: “If it is hot and Brian is outside, he will be sweaty.”

H and O —> S

Negate: “If it is hot and Brian is outside, he will be sweaty.”

/S —> /H or /O

“If Brian is not sweaty, then it must be not hot or Brian must not be outside.”

Negate: A and B —> C

/C —> /A or /B

(remember that negated “and” becomes “or”)

Translate: “If Susan is feeling unwell, she will call in sick to work and stay home.”

U —> C and H

Negate: “If Susan is feeling unwell, she will call in sick to work and stay home.”

/C or /H —> /U

“If Susan doesn’t call in sick, or if she doesn’t stay home, then she is not feeling unwell.”

Negate: A —> B and C

/C or /B —> /A

(remember that negated “and” becomes “or”)

Translate: “If Talissa has a son, she will name him John or Dan.”

S —> J or D

Negate: “If Talissa has a son, she will name him John or Dan.”

/J and / D —> /S

“If Talissa doesn’t name a child John and doesn’t name a child Dan, then she didn’t have a son.”

Negate: A —> B or C

/B and /C —> /A

(remember that negated “or” becomes “and”)

Translate: “If I eat candy or rocks for breakfast, I won’t feel well.”

C or R —> /W

Negate: “If I eat candy or rocks for breakfast, I won’t feel well.”

W —> /C and /R

“If I am feeling well, then I didn’t eat candy for breakfast and I didn’t eat rocks for breakfast.”

Negate: A or B —> C

/C —> /A and /B

(remember that negated “or” becomes “and”)

“Not all” or /All

“Some not” or /Some

Translate: Not all teachers love apples.

T ← some → /LA

Some teachers do not love apples