The if-then relationship — the backbone of LSAT reasoning
Watch this first. Then move to the practice tabs.
Video: Sufficient & Necessary Conditions — coming soon
Guided Practice Video: Sufficient Indicators — coming soon
"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 employee must complete the training."
What is the sufficient condition?
"Every" introduces the sufficient condition. Being an employee is enough to trigger the requirement. Employee → Must complete training.
"Whenever she studies, she passes."
What is the sufficient condition?
"Whenever" introduces the sufficient condition. Studying is enough to guarantee passing. Studies → Passes.
"If a student is enrolled, then they have paid tuition."
A student is enrolled. What can we conclude?
The sufficient condition is met, so the necessary must follow. Enrolled → Paid tuition. The student is enrolled, so they must have paid.
Guided Practice Video: Necessary Indicators — coming soon
"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.
"If a student is enrolled, then they have paid tuition."
A student has paid tuition. What can we conclude?
Knowing the necessary condition is true tells us nothing. Enrolled → Paid 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.
Video: The Contrapositive — coming soon
Guided Practice Video: Contrapositive — coming soon
"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."
A book has not been edited. What can we conclude?
This is the contrapositive in action. Published → Edited. Contrapositive: NOT edited → NOT published. The book hasn't been edited, so it can't have been published.
"If it snows, then schools close."
Schools did not close. What can we conclude?
Contrapositive: NOT close → NOT snow. If schools didn't close, it didn't snow. (B) is impossible — the original says snow guarantees closures.
"If it snows, then schools close."
It did not snow. What can we conclude?
Negating the sufficient tells us nothing. Snow → Close. We know it didn't snow, but schools could still close for another reason. The contrapositive only works when we negate the necessary side.
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
Then, 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.