CONDITIONAL LOGIC BASICS

The if-then relationship — the backbone of LSAT reasoning

What Are Sufficient & Necessary Conditions?

Watch this first. Then move to the practice tabs.

Guided Practice: Sufficient Indicators

Tip: Try the questions below first, then come back and watch the video.
Identify

"If it rains, then the ground is wet."

What is the sufficient condition?

AIt rains
BThe ground is wet
Explanation

"If" introduces the sufficient condition. Rain is enough to guarantee wet ground. Rain Ground is wet.

Identify

"Every dog that goes to obedience school is well behaved."

What is the sufficient condition?

AGoing to obedience school
BBeing well behaved
Explanation

"Every" introduces the sufficient condition. Going to obedience school is enough to guarantee being well behaved. Obedience school Well behaved.

Identify

"Whenever she studies, she passes."

What is the sufficient condition?

AShe passes
BShe studies
Explanation

"Whenever" introduces the sufficient condition. Studying is enough to guarantee passing. Studies Passes.

Apply

"An enrolled student must pay tuition."

A student is enrolled. What can we conclude?

AThey must pay tuition.
BWe cannot conclude anything.
Explanation

The sufficient condition is met, so the necessary must follow. Enrolled Pay tuition. The student is enrolled, so they must pay tuition.

Guided Practice: Necessary Indicators

Tip: Try the questions below first, then come back and watch the video.
Identify

"You can drive only if you have a license."

What is the necessary condition?

AYou can drive
BYou have a license
Explanation

"Only if" introduces the necessary condition. Having a license is required for driving. Drive License. Be careful: "if" and "only if" point in opposite directions.

Identify

"Graduation requires completing all coursework."

What is the necessary condition?

ACompleting all coursework
BGraduation
Explanation

"Requires" introduces the necessary condition. Coursework is required for graduation. Graduation Completed coursework.

Identify

"Success depends on preparation."

What is the necessary condition?

ASuccess
BPreparation
Explanation

"Depends on" introduces the necessary condition. Preparation is required for success. Success Preparation.

Apply

"An enrolled student must pay tuition."

A student has paid tuition. What can we conclude?

AThey are enrolled.
BWe cannot conclude anything.
Explanation

Knowing the necessary condition is true tells us nothing. Enrolled Pay tuition. We know they paid, but paying doesn't guarantee enrollment — maybe they paid and withdrew, or payment is just one of several requirements. The arrow only goes one direction.

The Contrapositive

Flip the direction and negate both sides. Watch this first.

Guided Practice: Contrapositive

Tip: Try the questions below first, then come back and watch the video.
Contrapositive

"If it rains, then the ground is wet."

What is the contrapositive?

AIf the ground is not wet, then it did not rain.
BIf it does not rain, then the ground is not wet.
Explanation

Flip and negate. Rain → Wet ground becomes: NOT wet ground → NOT rain. If the ground isn't wet, it couldn't have rained. (B) negates the sufficient without flipping — that's not valid.

Contrapositive

"You can drive only if you have a license."

What is the contrapositive?

AIf you cannot drive, then you do not have a license.
BIf you do not have a license, then you cannot drive.
Explanation

First, set up the original: Drive → License. Then flip and negate: NOT license → NOT drive. If you don't have a license, you can't drive. (A) negates the sufficient without flipping — that's not valid.

Contrapositive

"If a book is published, then it has been edited."

What is the contrapositive?

AIf it has been edited, then it has been published.
BIf it has not been edited, then it has not been published.
Explanation

Flip and negate. Published → Edited becomes: NOT edited → NOT published. (A) flips the direction but doesn't negate — knowing a book was edited doesn't mean it was published.

Contrapositive

"If it snows, then schools close."

What is the contrapositive?

AIf it did not snow, then schools did not close.
BIf schools did not close, then it did not snow.
Explanation

Flip and negate. Snow → Close becomes: NOT close → NOT snow. If schools didn't close, it didn't snow. (A) negates the sufficient without flipping — schools could still close for other reasons.

Contrapositive

"An enrolled student must pay tuition."

What is the contrapositive?

AIf a student is not enrolled, then they do not pay tuition.
BIf a student has not paid tuition, then they are not enrolled.
Explanation

Flip and negate. Enrolled → Pay tuition becomes: NOT pay tuition → NOT enrolled. (A) negates the sufficient without flipping — a student who isn't enrolled could still owe tuition for other reasons.

Quick reference for conditional logic. Bookmark this page and come back to it while practicing.

The Conditional
Structure

Sufficient Necessary

If the sufficient happens, the necessary must follow.

Common Triggers
Sufficient Condition

If, All, Every, Whenever, When, People who, Each, Any, The only

Necessary Condition

Must, Only if, Only when, Requires, Necessary, Depends on

The Contrapositive
How to form it

Flip the direction and negate both sides.

A B   becomes:

NOT B NOT A

✓ Always valid — the contrapositive is logically identical to the original.

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