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Find a sufficient assumption by completing a proof and rejecting additions that leave a possible countercase.
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.
Select an added premise that makes the exact conclusion follow, preserve conditional direction and quantity, and distinguish a complete repair from a merely helpful or necessary condition.
First identify the conclusion and its stated support, as in the argument-parts lesson. Then recall the necessary-assumption test: deny a candidate and look for failure of required support. This lesson asks a different question. Accept one proposed addition and see whether the premises now guarantee the conclusion. Do not apply the previous test just because the question contains assumption.
| Term | What it means |
|---|---|
| Sufficient assumption | An addition that makes the conclusion follow when combined with the stated premises. |
| Conditional | A rule of the form if A, then B: having A guarantees B within the rule's scope. |
| Converse | The reversed rule if B, then A; it does not automatically follow from if A, then B. |
| Countercase | A possible situation with true premises and a true proposed addition but a false conclusion. |
| Contrapositive | If not B, then not A, which preserves the force of if A, then B. |
| Quantifier | A scope word such as every, some or none; some means at least one here. |
A sufficient assumption is an added premise that, together with the stated premises, makes the conclusion follow. Imagine accepting both the original evidence and the candidate. Can the conclusion still be false? If a coherent case remains, the addition is not sufficient. If the conclusion follows by a complete sequence of justified steps, the addition is sufficient. This is a test of the argument with an addition, not a claim that the original argument was already valid.
Suppose an archive's rule is that every cataloged photograph can be requested. Photograph Q has a reference number. The conclusion says Q can be requested. Adding that every photograph with a reference number is cataloged supplies a route: Q has a reference number, so Q is cataloged, so Q can be requested. Adding that most numbered photographs are cataloged leaves Q free to be an exception. The second addition might help, but it does not settle this conclusion.
Hold the original premises fixed and test one candidate at a time. The candidate need not be the weakest imaginable repair; a broad rule can suffice. It need not be necessary either, since another rule could establish the same conclusion. You are looking for an offered addition that completes the proof. These exercises use compatible additions, so a contradiction with the premises is not being offered as a useful argument repair.
Another way: picture
Read the support map as a sequence of labeled steps: numbered photograph; added link to cataloged photograph; existing link to request permission. An arrow licenses travel in its stated direction. It does not become a two-way arrow merely because the same two labels occur at its ends.
Another way: steps
Separate premises and conclusion. Locate the missing link or missing condition. Add a candidate without changing the premises. Derive the conclusion one step at a time. If a step needs another unstated rule, try a case where that rule fails. Reset before testing the next candidate.
If a file is approved, then it is released. Approval is sufficient for release under this rule. Release is necessary for approval under this rule: an approved but unreleased file would violate it. Yet a released file need not have been approved; the rule allows some other route to release. Do not silently change if into if and only if.
Only if points to a requirement. 'A file is released only if it is approved' means that release requires approval. Knowing approval alone does not establish release from that sentence. Compare it with 'A file is released if it is approved,' which does license approval to release. Rewrite the rule as a full if-then sentence before using it. Word order can change without changing direction: 'Only approved files are released' still makes approval a requirement of release.
The contrapositive preserves the original direction of constraint. From 'if approved, then released,' not released implies not approved. Otherwise we would have an approved file with no release, exactly what the rule excludes. But not approved does not imply not released. That mistaken inverse removes a condition without ruling out other routes to the result. In a repair problem, a valid negative inference may supply the intermediate fact needed for the added rule.
A conclusion about a particular person needs a route covering that person. 'Some trained people qualify' leaves a named trained person possibly outside the qualifying group. 'Most trained people qualify' still allows an exception. A conclusion about every person needs a rule covering every relevant person, or enough individual facts to cover them all. A plausible trend does not supply that coverage.
An existential conclusion needs a witness: at least one thing that satisfies the description. From some members being designers and every designer having a portfolio, we can conclude that some members have portfolios. It is the same member through both steps. If we add that every portfolio holder qualifies, that member qualifies too. Merely knowing that some portfolio holders in another group qualify may concern entirely different people.
Do not carry the single-answer convention into a classification exercise. Several additions can each be sufficient. For example, both a universal rule linking portfolios to eligibility and a direct statement that some club members with portfolios are eligible can establish that some club members are eligible. The records ask you to judge every addition separately; they do not promise exactly one S. The five-option questions do have one correct answer.
A rule may require a combination. If training and a passed check jointly ensure authorization, training alone does not establish authorization. A passed check for that same person completes the stated rule. A check passed by someone else does not. Nor does a sentence saying authorization requires training: that sentence repeats a requirement without granting authorization.
An either-or premise offers another pattern. If a delivery must use Route A or Route B, or both, ruling out Route A leaves Route B. Merely establishing Route A does not establish Route B, and inclusive or does not mean both. If the desired conclusion concerns a property of the surviving route, such as permission to use it after dark, the added premise must establish that property as well.
Conclusions about what ought to happen or what is permitted also need a connecting rule. Facts about reduced noise do not by themselves entail a council recommendation. A stated policy can connect specified facts to a recommendation; an addition can then supply a missing policy condition. Follow the policy as given for the exercise. Do not import your own preferences or an unstated legal rule.
A necessary-assumption question asks what the reasoning cannot lose. A sufficient-assumption question asks what makes the conclusion follow when added. A strengthening question asks for improved support and can accept evidence that leaves uncertainty. Read the requested task before evaluating the answer's strength. The same addition may be sufficient for a narrow conclusion yet insufficient for a broader one.
Suppose one usable room would satisfy a meeting's room requirement. Both rooms being usable is sufficient for that requirement but is not necessary: one may fail while the other works. The previous lesson's negation test would reject the both-rooms claim as necessary, correctly. That rejection does not show it is insufficient. Conversely, permission to use a room may be necessary for holding the meeting there without guaranteeing that a suitable room is available.
A reliable answer check has two parts. Give a forward derivation for your chosen addition, identifying which sentence licenses each move. For a tempting rival, describe one surviving countercase while keeping its addition and all premises true. Avoid declaring a candidate insufficient merely because it sounds unusual or broad. Also avoid concluding that the argument is sound in the real world just because the conditional proof works: truth of its assumptions is a separate issue.
When reading a workplace recommendation, separate factual premises from the rule used to reach a decision. Write the exact recommendation in one line. Then ask which added fact or rule would complete that particular inference. This can expose an unstated policy or a missing eligibility condition without claiming the policy itself is justified. The transfer memos here ask for that logical audit; they are invented situations, not advice about actual institutions.
After a missed practice item, record the failed move: reversed direction, missing half of a condition, a different population, or a plausible extra without a connecting rule. Write a countercase to the chosen wrong addition and a short forward derivation for the correct one. Revisit the argument the next day without the answer choices. That retrieval checks whether you learned the relation rather than the position of an option.
The automatic records grade classifications and recognition of a supplied proof. Review the supplied derivation against four criteria: it preserves all premises, applies each rule in its stated direction, keeps the same people or objects through the chain, and reaches the exact conclusion without an extra hidden premise. Identify where a rejected proof fails one of those criteria, then use the feedback to check your diagnosis. No original writing submission or outside reader is required. All questions are original preparation exercises, not LSAC items or a prediction of a test score.
A candidate can be relevant without being sufficient. Most is not all; some group members need not include the named person. If and only if have different directions, and denying an antecedent is not contraposition. An answer may be stronger than necessary and still suffice. Test one addition at a time, and never manufacture a new rule to connect an attractive detail to the conclusion.
Read the argument and target.
A Richmond depot dispatches every packed parcel. Parcel H has been labeled. Therefore H is dispatched.
The missing step is from labeled to packed, not from dispatched back to labeled.
Compare five additions.
A: Every packed parcel is labeled. B: Every labeled parcel is packed. C: Some labeled parcels are packed. D: Every dispatched parcel is labeled. E: H has a red label.
B supplies the missing forward link. A and D run backward from a later property; C may concern another parcel; E lacks a color-to-packing rule.
Apply the complete repair.
Choose B. H is labeled; therefore H is packed; therefore H is dispatched.
The first move uses the addition and the second uses the original rule. No further assumption is needed.
Keep a rival true while the conclusion fails.
For C, other labeled parcels can be packed while H is labeled but unpacked and undispatched.
That case preserves C and the depot's rule, so C is insufficient despite its relevant wording.
Read the authorization rule.
A Trenton studio grants access to anyone who has both completed induction and booked a slot. Ellis completed induction. Therefore Ellis is granted access.
Induction is established; the original rule does not say induction alone suffices.
Compare five proposed additions.
A: Everyone granted access completed induction. B: Some people who completed induction booked slots. C: Ellis likes the studio. D: Ellis booked a slot. E: Ellis gets access only if Ellis books a slot.
D supplies the missing fact for Ellis. A and E give requirements of access, B can concern others, and C does not trigger the rule.
Derive the access conclusion.
Choose D: Ellis has induction and a booking, so the studio's rule grants Ellis access.
Both conditions concern the same person and together activate the stated sufficient condition.
Reject the only-if trap.
E allows Ellis to have no booking and no access. Completing induction can still be true in that case.
A requirement of access does not establish that the requirement has been met.
Read the existential argument.
Some volunteers at a Fresno garden are trained seed collectors. Every trained seed collector can identify mature seeds. Therefore some volunteers there may supervise seed collection.
The conclusion requires at least one eligible supervisor among those volunteers.
Compare five additions.
A: Anyone who may supervise can identify mature seeds. B: Some people in another garden who identify mature seeds may supervise. C: Anyone who identifies mature seeds may supervise seed collection. D: Every volunteer in this garden collects seeds. E: The garden has a tool shed.
C links an established ability to permission. A reverses it; B may have a disjoint group; D adds activity without permission; E is background.
Locate a witness in the target group.
The some-volunteers premise guarantees at least one trained volunteer in this garden, even though it does not name that person.
Universal rules alone need not establish that anyone exists. This existential premise supplies the person to whom the rules can apply.
Carry a witness through the chain.
Choose C. At least one volunteer is trained, so that volunteer identifies mature seeds and, by C, may supervise.
The existential premise supplies an actual member of the target group; the two universal rules apply to that same member.
Test the different-group alternative.
B permits every volunteer here to lack permission while a person at the other garden has permission.
True information about another group does not establish the required overlap in this one.
Translate the stated rule.
A Mesa archive lends an object only if it is insured. Object T is not insured. The conclusion says T must remain on site.
Lending requires insurance. Not insured therefore rules out lending, but does not yet establish where T must remain.
Supply a sufficient added rule.
Every object the archive does not lend must remain on site.
This connects the intermediate fact we can prove to the conclusion we need.
Finish and check the derivation.
Original argument: A Dayton center received an application from Mara. Its rules grant a desk to anyone whose application is accepted. The director concludes that Mara will be granted a desk. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Every participant in an Albany seminar submitted a draft. Every submitted draft received comments. The organizer concludes that every seminar participant is eligible for a follow-up session. Proposed additions: (1) Anyone who submitted a draft that received comments is eligible for the follow-up session. (2) Everyone eligible for the follow-up session submitted a draft that received comments. (3) Some participants who submitted drafts are eligible for the follow-up session. (4) Every seminar participant submitted a draft before noon. (5) The organizer saved a copy of the seminar announcement. Complete the proof method with the number of the sufficient addition.
Separate the premises from the target.
Keep every stated premise and the conclusion's exact scope.
The added claim must prove this conclusion rather than a weaker substitute.
Supply a complete connection.
Sufficient addition: bridge.
Use a rule in its stated direction and cover every missing condition.
Check the resulting proof.
Trace each justified step from the given facts to the exact conclusion.
If an extra unstated rule is still needed, the repair is not yet sufficient.
Some members of a Madison club are illustrators. Every illustrator in the club keeps a portfolio. The secretary concludes that some club members are eligible for its exhibition. Proposed additions: (1) Every club member is an illustrator. (2) The club owns a projector. (3) Every club member who keeps a portfolio is eligible for the exhibition. (4) Every eligible club member keeps a portfolio. (5) Some club members who keep portfolios are eligible for the exhibition. Test each addition SEPARATELY with the original premises. Enter S if it is sufficient for the conclusion, or U if a gap remains. More than one may be S. Then enter the number of the valid proof from this list: (1) Every eligible member keeps a portfolio, so any portfolio holder must be eligible. (2) The club owns a projector, so at least one member is eligible. (3) At least one club member is an illustrator and hence keeps a portfolio; the added universal rule makes that member eligible. The proof may use the sufficient addition it describes. These analysis records are a practice format, not an official LSAT response format.
| Analysis entry | S or U; number for the last row |
|---|---|
| Addition 1 | |
| Addition 2 | |
| Addition 3 | |
| Addition 4 | |
| Addition 5 | |
| Valid proof (number) |
Original argument: A Toledo archive labels every digitized letter searchable. Letter K has been transcribed. The archivist concludes that Letter K is searchable. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Original argument: An Omaha workshop authorizes any volunteer who has both completed training and passed its safety check. Noor has completed training. The coordinator concludes that Noor is authorized. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Original argument: A Boise museum routes every new acquisition to either its upstairs room or its ground-floor room, possibly both. Object R is a new acquisition. The curator concludes that R is routed to the ground-floor room. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Original argument: A Salem council's stated policy is to recommend every proposal that reduces noise without increasing fees. Proposal L reduces noise. A member concludes that the policy calls for recommending L. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Original argument: A Tulsa lab releases a sample only if its seal is intact. Sample V's seal is not intact. An assistant concludes that V must remain in the secure cabinet. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Original argument: Every participant in an Albany seminar submitted a draft. Every submitted draft received comments. The organizer concludes that every seminar participant is eligible for a follow-up session. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Original argument: A Dayton center received an application from Mara. Its rules grant a desk to anyone whose application is accepted. The director concludes that Mara will be granted a desk. Which statement, if added to the stated premises, makes the conclusion follow? Evaluate each candidate separately.
Every parcel routed through Depot H receives a tracking code. Parcel M bears a blue seal. The dispatcher concludes that M receives a tracking code. Which added rule makes the conclusion follow?
An Erie records officer writes: 'Some files in this batch are signed. Every signed file is authenticated. Therefore some files in this batch must be retained.' Evaluate the stated retention claim without importing an outside records policy. Proposed additions: (1) Some authenticated files outside this batch must be retained. (2) Every file in this batch is signed. (3) The batch arrived in a green folder. (4) Every authenticated file must be retained. (5) Every file that must be retained is authenticated. Test each addition SEPARATELY with the original premises. Enter S if it is sufficient for the conclusion, or U if a gap remains. More than one may be S. Then enter the number of the valid proof from this list: (1) A signed file exists in this batch and is authenticated; the added rule makes that same file one that must be retained. (2) Files requiring retention are authenticated, so all authenticated files require retention. (3) A file outside this batch requires retention, so a file inside this batch must require retention. The proof may use the sufficient addition it describes. These analysis records are a practice format, not an official LSAT response format.
| Analysis entry | S or U; number for the last row |
|---|---|
| Addition 1 | |
| Addition 2 | |
| Addition 3 | |
| Addition 4 | |
| Addition 5 | |
| Valid proof (number) |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Every registered entrant in a Hartford exhibition has a numbered badge. Every numbered badge is valid for entry. Inez registered. The organizer concludes that Inez may bring a guest. Proposed additions: (1) Anyone holding a badge valid for entry may bring a guest. (2) Anyone who may bring a guest holds a badge valid for entry. (3) Some holders of badges valid for entry may bring guests. (4) Inez registered before the deadline. (5) Inez has attended an exhibition before. Test each addition SEPARATELY with the original premises. Enter S if it is sufficient for the conclusion, or U if a gap remains. More than one may be S. Then enter the number of the valid proof from this list: (1) People with guest permission hold valid badges, so anyone holding a valid badge has guest permission. (2) Some valid badge holders have guest permission, so Inez has it. (3) Inez has a numbered badge, hence a badge valid for entry; the added rule grants guest permission to anyone with such a badge. The proof may use the sufficient addition it describes. These analysis records are a practice format, not an official LSAT response format.
| Analysis entry | S or U; number for the last row |
|---|---|
| Addition 1 | |
| Addition 2 | |
| Addition 3 | |
| Addition 4 | |
| Addition 5 | |
| Valid proof (number) |
Tomorrow, recall the difference between denying a necessary assumption and adding a sufficient assumption. Reconstruct one proof without notes and give a countercase to its reversed rule. Next: strengthening, where an improvement in support can be enough even without a guarantee.
14. Finish a proof using a necessary condition, step 3
T is not insured, so T is not lent. The added rule then requires T to remain on site.
Reversing the addition would leave open an unloaned object being moved elsewhere. The original rule alone establishes only the no-loan fact.