The if-then relationship — the backbone of LSAT reasoning
Watch this first. Then move to the practice tabs.
"If it rains, then the ground is wet."
What is the sufficient condition?
"If" introduces the sufficient condition. Rain is enough to guarantee wet ground. Rain → Ground is wet.
"Every dog that goes to obedience school is well behaved."
What is the sufficient condition?
"Every" introduces the sufficient condition. Going to obedience school is enough to guarantee being well behaved. Obedience school → Well behaved.
"Whenever she studies, she passes."
What is the sufficient condition?
"Whenever" introduces the sufficient condition. Studying is enough to guarantee passing. Studies → Passes.
"An enrolled student must pay tuition."
A student is enrolled. What can we conclude?
The sufficient condition is met, so the necessary must follow. Enrolled → Pay tuition. The student is enrolled, so they must pay tuition.
"You can drive only if you have a license."
What is the necessary condition?
"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.
"Graduation requires completing all coursework."
What is the necessary condition?
"Requires" introduces the necessary condition. Coursework is required for graduation. Graduation → Completed coursework.
"Success depends on preparation."
What is the necessary condition?
"Depends on" introduces the necessary condition. Preparation is required for success. Success → Preparation.
"An enrolled student must pay tuition."
A student has paid tuition. What can we conclude?
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.
Flip the direction and negate both sides. Watch this first.
"If it rains, then the ground is wet."
What is the contrapositive?
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.
"You can drive only if you have a license."
What is the contrapositive?
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.
"If a book is published, then it has been edited."
What is the contrapositive?
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.
"If it snows, then schools close."
What is the contrapositive?
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.
"An enrolled student must pay tuition."
What is the contrapositive?
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.
Sufficient → Necessary
If the sufficient happens, the necessary must follow.
If, All, Every, Whenever, When, People who, Each, Any, The only
Must, Only if, Only when, Requires, Necessary, Depends on
Flip the direction and negate both sides.
A → B becomes:
NOT B → NOT A
✓ Always valid — the contrapositive is logically identical to the original.