Conditional Reasoning I: Sufficient vs Necessary & the Contrapositive
Recap: A Prerequisite, Not Just Another Topic
This is not a day in a sequence of independent topics — conditional logic is infrastructure that Sufficient Assumption, Necessary Assumption, Must Be True, Flaw, and Parallel Reasoning are all built on top of. Get the mechanics wrong today and every one of those question types (spread across Weeks 5–10) inherits the error.
CS Bridge
A conditional is p → q. Its contrapositive, ¬q → ¬p, is logically identical — just like De Morgan's laws give you an equivalent form of a boolean expression. Two classic bugs to watch for, because they're exactly the errors the test exploits: affirming the consequent (from p → q and q, wrongly concluding p — the "mistaken reversal") and denying the antecedent (from p → q and ¬p, wrongly concluding ¬q — the "mistaken negation"). Also: natural-language "if" is often used loosely as biconditional in everyday speech ("if you're good, I'll get you ice cream" implies the reverse too) — the LSAT never means it that way. Read every conditional as strictly one-directional unless the stimulus explicitly says otherwise.
1. Sufficient Indicators
If, when, every, all, any, whenever — these introduce the sufficient condition (the antecedent, the "p"). "If it rains, the game is cancelled" → rain → cancelled.
2. Necessary Indicators
Only if, requires, must, depends on, needs — these introduce the necessary condition (the consequent, the "q"). "The game will proceed only if the field is dry" → proceed → dry. Note the direction: the thing before "only if" is the sufficient side, not the necessary side — this is the single most commonly reversed pattern on the test.
3. Diagramming Quickly
Use the minimum notation that keeps you accurate under time pressure: an arrow and short abbreviations. Rain → Cxl. Don't over-formalize with full symbolic logic notation — that's a CS instinct that costs time here without buying extra accuracy on a test that rewards speed as much as rigor.
4. The Contrapositive
Flip and negate both sides: p → q becomes ¬q → ¬p. This is the only guaranteed valid inference you can draw from a single conditional standing alone. "If it rains, the game is cancelled" guarantees "if the game was not cancelled, it did not rain" — and nothing else.
5. Reversal and Negation Errors
From rain → cancelled, you cannot conclude "if it didn't rain, the game wasn't cancelled" (negation — the game could be cancelled for other reasons) and you cannot conclude "if the game was cancelled, it rained" (reversal — again, other causes are possible). Both of these show up constantly as wrong answer choices and, in Flaw questions, as the flaw itself.
6. Where This Shows Up Later
Necessary Assumption questions often hinge on identifying an unstated necessary condition the argument's conclusion secretly depends on. Sufficient Assumption questions ask you to supply a missing conditional link that would make the argument airtight. Must Be True questions frequently chain two or more conditionals together. Flaw questions often are exactly "the argument commits a mistaken reversal/negation." File all of that away — you'll be back here constantly.
Practice items on this page are curriculum-authored in LSAT style; they are not official LSAC questions. Real drilling happens on LawHub — see the assignment below.
Original Practice Items
Q1. Translate: "You may enroll in the advanced seminar only if you have completed the introductory course."
Q2. Given "Advanced → Intro," which is the valid contrapositive?
Q3. A student did NOT complete the intro course. What, if anything, follows about the advanced seminar (given "Advanced → Intro")?
Official Drill Assignment
LawHub free lessons on conditional reasoning. No PT sections used yet — the diagnostic is Saturday.
Peek into Tomorrow
Tomorrow maps the entire territory of LR question types before the diagnostic, so that when you sit the diagnostic Saturday, you at least recognize what each stem is asking — even for the type-specific technique you haven't learned yet.