LSAT conditional logic: sufficient, necessary, and the contrapositive

Conditional statements are the closest thing the LSAT has to formal machinery, and they turn up everywhere: Inference questions that hinge on a chain, Flaw questions built on a reversal, Assumption questions where the gap is a missing link. Getting comfortable here pays across the whole section.

Sufficient and necessary

A conditional says: if this, then that. The first part is SUFFICIENT — knowing it is enough to guarantee the second. The second is NECESSARY — it has to be true whenever the first is.

"If the bridge is open, the ferry does not run." Bridge open is sufficient: learn it and you know the ferry is idle. Ferry not running is necessary: it must hold whenever the bridge is open. What you cannot do is run it backwards — a ferry sitting idle does not tell you the bridge is open, because it might be idle for a dozen other reasons.

The words that signal which side is which

• Introduce the SUFFICIENT side: if, when, whenever, any, all, every, each, people who.
• Introduce the NECESSARY side: then, only, only if, must, requires, depends on, is essential to, unless.
• "Only" is the one that catches people. "Only members may enter" does not mean members may enter — it means entering requires membership. Being a member is necessary, not sufficient.
• "Unless" means "if not". "You cannot enter unless you have a pass" becomes: if you do not have a pass, you cannot enter — equivalently, entering requires a pass.
• "No" and "none" are conditionals too. "No reptiles are warm-blooded" is: if reptile, then not warm-blooded.

The contrapositive is the only valid flip

From "if A then B", exactly one other statement is guaranteed: if not B, then not A. Negate both sides and reverse them. That is the contrapositive, and it is always true when the original is.

Two other flips look similar and are both invalid. "If B then A" is the REVERSAL. "If not A then not B" is the NEGATION. Neither follows, and the exam tests exactly this — a Flaw answer describing an argument that "takes a condition sufficient for an outcome to be necessary for it" is naming a reversal.

Back to the bridge: from "if the bridge is open, the ferry does not run", the contrapositive is "if the ferry is running, the bridge is not open". That one is guaranteed. "If the ferry is not running, the bridge is open" is the reversal and is worth nothing.

Chains, and where they break

Conditionals link: A → B and B → C give you A → C. Long chains are common in Inference questions, and the credited answer is often just a link two or three steps down one, or the contrapositive of the whole thing.

They break on a mismatch. A → B and C → D do not chain unless B and C are actually the same idea, and a great deal of test writing lives in making two similar-sounding terms not quite identical. Before joining links, check the terms are the same term.