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Use precise negation to distinguish a necessary assumption from a helpful addition, an excessive guarantee or an irrelevant claim.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Identify a required unstated condition, deny it without changing its scope, and explain why that denial defeats the author's reasoning rather than merely making the situation less favorable.
In the previous lesson you separated the main conclusion from its reasons and any intermediate conclusion. Do that first here. A sentence about what someone should do is not automatically the conclusion, and a claim beginning with therefore may still support a further claim. Test an assumption against the main inference the question asks about.
| Term | What it means |
|---|---|
| Necessary assumption | An unstated condition required by the reasoning; its denial defeats required support. |
| Sufficient assumption | An added claim which, with the premises, makes the conclusion follow; it can be stronger than needed. |
| Negation | The contradictory claim: true exactly when the original claim is false. |
| Scope | The people, objects, time and amount a claim covers, including all, some and none. |
| Counterexample | A case that defeats a universal claim; one qualifying exception is enough. |
| Support failure | Loss of the argument's offered basis, which is different from proving its conclusion false. |
A necessary assumption is an unstated condition on which the reasoning depends. The author may not consciously think about it, and it need not settle the whole argument. The question is whether the offered support can do its intended work without that condition. A claim that makes the conclusion sound more attractive is not automatically required.
Suppose a mobile clinic expects a new booking page to let some patients book directly online. The page must be accessible to at least some patients who could use it. It does not have to be accessible to every person in the city. Deny the limited condition: no potential patient can access it. The proposed direct-booking route now fails. Deny universal access instead: someone cannot access it. That leaves other people able to book, so universal access was too strong.
This is the negation test. Hold the stated evidence fixed, make the candidate false, and ask whether a required link in the argument fails. A necessary assumption passes that test. Do not add a new rescue premise or demand that the candidate alone prove the conclusion. Several assumptions may be necessary; one question asks you to identify the needed one among its options.
Another way: picture
Think of a route from evidence to conclusion with a required crossing. Removing a necessary crossing blocks that route. Adding a comfortable waiting area might improve the journey, but its absence need not block passage. The metaphor concerns support, not the truth of the destination claim.
Another way: steps
Identify evidence and conclusion. Locate the unstated link. Negate one candidate exactly. Keep the evidence fixed and trace the effect. If the required support fails, retain the candidate; if the reasoning survives its denial, reject it. Reset before testing the next option.
Negation is not an instruction to invent the most dramatic opposite. 'All members can log in' is false if at least one member cannot log in. It need not be the case that nobody can. 'Some members can log in' is false only when no members can. Here some means at least one, not necessarily some but not all. 'No members can log in' is denied by at least one who can. Keep the same members, system and time throughout.
For 'A and B,' denial requires at least one of them to be false. For 'A or B' in its inclusive sense, denial requires both to be false. 'A and B will not both fail' is denied by both failing, not by either one failing. For a rule 'If A, then B,' the countercase is A together with not B; reversing the rule does not deny it. Start with 'It is not the case that ...' when the wording feels difficult, then express that precise contradiction naturally.
Boundaries count. The denial of 'less than four dollars on every sale' includes a sale costing exactly four dollars. Greater than four misses equality. A denial that is too strong can make an optional condition appear necessary by adding damage the original negation does not require.
Assume the stated premises for the task. You are not being asked to fact-check a hypothetical business or reject an observation you dislike. Locate the step the evidence does not establish: audience to access, possession to compatibility, lower totals to a lower rate, or revenue to net benefit. Then deny a candidate about that step and follow the consequences.
If an author attributes lower total resource use to greater efficiency, the entire fall must not be explained solely by less activity. Suppose the activity did fall: that alone does not defeat the efficiency explanation, because both changes could occur together. Suppose reduced activity entirely explains the fall: the total alone no longer establishes improved efficiency. The distinction is between a partial complication and removal of the offered basis.
Do not make all candidates false at once. Each receives a separate test. An unrelated falsehood elsewhere in the scenario does not tell you whether this candidate is necessary. After evaluating one denial, return to the original evidence before trying the next.
A sufficient assumption closes the inferential gap when added to the premises. A necessary assumption is something the inference cannot lose. These can coincide, but they need not. If a plan needs at least one usable route, both routes being usable would be more than enough for that particular requirement. Yet both being usable is not necessary: one route may fail while the other works.
A stronger claim can contain a necessary condition and still be the wrong answer. 'Every resident sees the notice' includes reaching potential participants, but its denial allows one resident to miss it while many potential participants see it. Test the whole option, not a weaker claim hidden inside it. Likewise, an additional source of evidence may support the conclusion without being assumed in the author's existing route.
False assumptions need not make the conclusion false. A study may reach the right result using an unreliable measurement. Denying measurement reliability undercuts that evidential route even if another study could establish the result. The negation test asks about this argument; it does not ask you to disprove every conceivable independent justification.
Write a short because sentence after choosing: 'The argument needs this because, if it were false, ...'. Complete it with the specific failed connection. Saying 'the argument gets weaker' is too vague: the denial of a merely helpful extra may also remove some support without eliminating anything essential. State why the author cannot make the particular move with the offered evidence.
Compare the other options with the same discipline. Does a universal claim exceed a limited conclusion? Does an attractive improvement add a separate reason? Does a biographical or decorative detail leave the inference untouched? Does an option describe an obstacle instead of an enabling condition? Then check your denial again. If two options appear necessary, inspect their scope, time and subject before choosing. Do not rely on a slogan that all strong words are wrong: a conclusion about every person can require a condition covering every person.
A necessary-assumption question asks what the reasoning depends on; a sufficient-assumption question asks what would make its conclusion follow. Read that difference before spending time on the options. Both question kinds can offer plausible bridge statements, but they apply different tests. Practise the distinction untimed until you can state it without borrowing the answer choices' wording.
For a wrong answer, write the exact denial you used. If you changed all into none, repair the negation before reassessing the argument. If the denial was accurate but only removed a convenient extra, identify the original support that remained. If you chose a background detail, return to the evidence and conclusion. An error log should name one of these reasoning errors rather than simply recording a letter.
The selected responses here check bounded judgments and identification of a denial among supplied statements. Use the supplied explanation to review four decisions: preserve the claim's scope, negate precisely, keep the evidence fixed and identify the failed link. Locate the first decision you missed, then retry the classification using that correction. No original writing submission or outside reader is required. These are original preparation exercises, not LSAC items or a prediction of a test score.
A claim can strengthen an argument without being required. An assumption can be necessary without proving the conclusion by itself. Denying all does not mean none, and denying not both means both. Keep the same time and population. A contradictory obstacle is not an assumption the author needs in support, and a possible alternate proof does not repair the stated inference automatically.
Read the original argument and question.
A Miami garden posts a notice at a nearby café. Since many customers read the noticeboard, the organizer predicts that some notice readers will join Saturday's work session because of the notice. Which assumption is required?
The claim concerns direct recruitment of some readers, not the whole neighborhood.
Inspect all five candidates.
A: Every customer will join. B: Some notice readers are able to join Saturday's session. C: Radio will also advertise the session. D: The café uses recycled napkins. E: All notice readers are unavailable on Saturday.
A demands more participation than claimed, C offers another publicity route, D is unrelated and E blocks the proposed route.
Negate the plausible limited condition.
Denial of B: no notice reader is able to join Saturday's session.
The exact denial of some is none; 'not every reader can join' would leave some able to participate.
Decide by tracing the failure.
Choose B: if every reader is unavailable, none can join through the proposed recruitment.
Denying A merely allows one customer not to join, so the limited claim can survive. No radio advertisement or recycled napkin is needed.
Read the original plan.
A Kansas City ensemble will give each musician a part in a format readable only by its new player. Each musician has a laptop, so the director concludes that everyone can read their part on their own laptop at rehearsal.
Laptop possession is the evidence; universal individual access is the conclusion.
Find the unproved connection.
Possessing a laptop does not establish that this player's format is readable on it.
The equipment must support the particular proposed method, not merely exist.
Compare the five options.
A: Every musician's laptop can run the player at rehearsal. B: Everyone owns the same laptop model. C: All musicians prefer screens. D: The director owns a laptop. E: Some musicians' laptops cannot run the player.
A supplies the needed compatibility. Identical models, a preference and the director's equipment are unnecessary; E describes a failure.
Negate all without turning it into none.
Denial of A: at least one musician's laptop cannot run the player at rehearsal.
A single inaccessible laptop is enough to defeat access for everyone on their own laptops.
Select and audit the universal answer.
Choose A even though it says every. Different compatible models and reluctant screen users could still read their parts.
The universal scope matches the conclusion, while the other claims are either stronger, irrelevant or incompatible.
Read the original business argument.
A Sacramento club sells a program for eight dollars and pays five dollars to print it. The treasurer concludes that every sale leaves positive profit after all attributable costs.
The conclusion concerns net profit on every sale, not merely revenue above printing cost.
Compute the available margin.
Eight minus five leaves three dollars before other attributable costs.
That remaining amount must cover any other sale-related costs before profit is positive.
Compare the five candidates.
A: There are no other costs. B: Other costs on every sale are below three dollars. C: Printing might get cheaper next year. D: The program has a glossy cover. E: Each sale also costs four dollars to process.
A is an unnecessary zero-cost guarantee, C is a future benefit, D is a design detail and E would eliminate profit.
Deny the bounded condition precisely.
Denial of B: at least one sale has other costs of three dollars or more.
The negation must include equality and needs only one exception to the every-sale claim.
Trace both the boundary and the stronger distractor.
At three dollars there is zero profit; above it there is a loss. But an extra cost of one dollar still leaves two dollars profit.
The first case defeats positive profit on every sale; the second shows that zero additional costs is not necessary.
State the justified selection.
Choose B and reject A, C, D and E for the specific reasons above.
The needed condition is the threshold that preserves positive margin, not the most favorable imaginable business arrangement.
Read the original inference.
A Seattle laundry reports lower total water use after installing a new washer. From that total alone, its owner concludes that water use per load has fallen.
Recall the first lesson: the per-load claim is the conclusion, while the lower total is the premise.
Identify and deny the candidate.
Candidate: fewer loads do not entirely explain the lower total. Denial: fewer loads entirely explain the lower total.
The question concerns whether the total supplies evidence for improved efficiency.
Explain what fails and what does not follow.
A bakery moves its proofing trays to a temperature-controlled cabinet and subsequently fewer loaves collapse. During the same period it also begins using a stronger flour. A coordinator concludes that the intervention caused the improvement, arguing that stable proofing temperature prevents excessive expansion. Which assumption is required by the stated mechanism?
A coastal rescue station adds reflective markers to its landing route and subsequently crews reach the dock faster at night. During the same period it also introduces a navigation refresher course. A coordinator concludes that the intervention caused the improvement, arguing that markers make the approach easier to identify in darkness. Which assumption is required by the stated mechanism?
A translation office adds a glossary check before delivery and subsequently clients report fewer terminology inconsistencies. During the same period it also assigns repeat clients to the same translator. A coordinator concludes that the intervention caused the improvement, arguing that a shared glossary catches conflicting renderings. Which assumption is required by the stated mechanism?
A bus depot installs a parts-location display and subsequently mechanics complete repairs sooner. During the same period it also hires an additional mechanic for each shift. A coordinator concludes that the intervention caused the improvement, arguing that less time is spent searching for replacement components. Which assumption is required by the stated mechanism?
A pottery workshop changes the drying schedule and subsequently fewer vessels crack. During the same period it also buys clay from a different supplier. A coordinator concludes that the intervention caused the improvement, arguing that more gradual drying reduces internal stress. Which assumption is required by the stated mechanism?
A public records office introduces a checklist for requests and subsequently fewer applications are returned incomplete. During the same period it also simplifies the application requirements. A coordinator concludes that the intervention caused the improvement, arguing that the checklist helps applicants supply required information. Which assumption is required by the stated mechanism?
A greenhouse adds screens over ventilation openings and subsequently fewer plants show insect damage. During the same period it also starts introducing predatory insects. A coordinator concludes that the intervention caused the improvement, arguing that screens prevent pest insects from entering. Which assumption is required by the stated mechanism?
A theater sends audiences a transport guide and subsequently fewer ticket holders arrive late. During the same period it also moves performances thirty minutes later. A coordinator concludes that the intervention caused the improvement, arguing that travel information helps audiences choose workable routes. Which assumption is required by the stated mechanism?
A fisheries laboratory uses a gentler tagging method and subsequently more tagged fish survive release. During the same period it also conducts releases in cooler water. A coordinator concludes that the intervention caused the improvement, arguing that reduced handling injury improves survival. Which assumption is required by the stated mechanism?
A city library places topic summaries on catalogue pages and subsequently readers find relevant books sooner. During the same period it also reorganizes its subject headings. A coordinator concludes that the intervention caused the improvement, arguing that summaries let readers distinguish closely related books. Which assumption is required by the stated mechanism?
A seed bank switches to moisture-sealed envelopes and subsequently more stored seeds germinate. During the same period it also begins collecting seeds later in the season. A coordinator concludes that the intervention caused the improvement, arguing that reduced moisture exchange preserves viability. Which assumption is required by the stated mechanism?
Answer three reserved questions without hints. These cases are separate from lesson practice.
A records office will save 28 staff minutes per application by accepting structured digital submissions instead of paper. Its director concludes that total staff time per application will fall. Digital submissions require a new verification step, whose duration the director has not reported. Apart from entry and verification, staff work will remain unchanged. Which assumption does the conclusion require?
A hall can hold at most 97 people. Exactly 87 tickets have been issued, but ticket holders may bring one guest without a ticket. An organizer says overcrowding is impossible because ticket sales are below capacity. Which fact is the organizer failing to account for?
A hall can hold at most 94 people. Exactly 84 tickets have been issued, but ticket holders may bring one guest without a ticket. An organizer says overcrowding is impossible because ticket sales are below capacity. Which fact is the organizer failing to account for?
Tomorrow, recall the denials of all, some and not both before looking at notes. State an unfamiliar argument's conclusion, test a candidate assumption, and explain exactly which support link fails. Next: a sufficient assumption that makes a conclusion follow, a different test from necessity.
14. Finish the rate-versus-total test, step 3
The total no longer establishes lower water use per load. This does not prove the machine is inefficient in every other situation.
Loss of the offered basis is enough to diagnose the argument's dependence; a separate investigation could answer another question.