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Sufficient Assumption

42 questions

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Question 41Question →

Below are five short arguments concerning the proposed Arcadia transit expansion. Each argument is logically incomplete because it commits a formal reasoning error or lacks a crucial premise. Match each incomplete argument to the specific sufficient assumption that perfectly bridges its logical gap.

Click a left item, then click its matching right item

Items

Argument 1: A municipal transit plan will secure federal funding only if it increases daily ridership. The Arcadia proposal centers on implementing automated ticketing, a measure that guarantees an increase in daily ridership. Therefore, the Arcadia proposal will successfully secure federal funding.
Argument 2: If a transit plan implements automated ticketing, it will eliminate toll jobs. Furthermore, eliminating toll jobs is a necessary condition for reducing carbon emissions. The Arcadia proposal will definitely eliminate toll jobs. Therefore, the Arcadia proposal involves implementing automated ticketing.
Argument 3: In order to reduce carbon emissions, a transit system must secure federal funding. The Arcadia proposal focuses on implementing automated ticketing, which unfortunately disqualifies it from securing federal funding. Therefore, the Arcadia proposal will eliminate toll jobs.
Argument 4: Most transit plans that increase daily ridership also succeed in reducing carbon emissions. By securing federal funding, the Arcadia proposal ensures that it will increase daily ridership. Therefore, the Arcadia proposal will ultimately implement automated ticketing.
Argument 5: Any transit plan that eliminates toll jobs will fail to secure federal funding unless it also increases daily ridership. The Arcadia proposal eliminates toll jobs but successfully increases daily ridership. Therefore, the Arcadia proposal will succeed in reducing carbon emissions.

Matches

Show answer & explanation

Answer

Argument 1 matches with the ridership-to-funding assumption. Argument 2 matches with the job-elimination-to-ticketing assumption. Argument 3 matches with the failed-funding-to-job-elimination assumption. Argument 4 matches with the ridership-to-ticketing assumption. Argument 5 matches with the combined job-elimination-and-ridership-to-emissions assumption.
Each correct assumption perfectly completes the deductive bridge by converting the argument's logical gap into a valid modus ponens deduction. By mapping the premises as conditional statements, we isolate the exact trigger needed to force the conclusion to be true.

Step-by-Step Solution

1
Identify the pool of repeating concepts across all arguments
Five concepts are used interchangeably: Automated Ticketing, Federal Funding, Daily Ridership, Toll Jobs, and Carbon Emissions.
Because all arguments use the same vocabulary, keyword matching will fail. Formal logic mapping is required.
2
Diagram the formal logic of Argument 1 and identify the gap
Premises: Funding -> Ridership; Ticketing -> Ridership. Fact: Arcadia has Ticketing (thus Ridership). Conclusion: Arcadia has Funding. Gap: Ridership -> Funding.
To fix the sufficient/necessary confusion, we must make the necessary condition sufficient.
3
Diagram Argument 2 and identify the gap
Premises: Ticketing -> Toll Jobs; Carbon -> Toll Jobs. Fact: Arcadia has Toll Jobs. Conclusion: Arcadia has Ticketing. Gap: Toll Jobs -> Ticketing.
To fix the Mistaken Reversal, we must connect the established fact (eliminating toll jobs) to the conclusion.
4
Diagram Argument 3 and identify the gap
Premises: Carbon -> Funding; Ticketing -> ~Funding. Fact: Arcadia has Ticketing (thus ~Funding). Conclusion: Arcadia eliminates Toll Jobs. Gap: ~Funding -> Toll Jobs.
We must bridge the intermediate deduction (~Funding) to the new term in the conclusion (Toll Jobs).
5
Diagram Argument 4 and identify the gap
Premises: Ridership -most-> Carbon; Funding -> Ridership. Fact: Arcadia has Funding (thus Ridership). Conclusion: Arcadia has Ticketing. Gap: Ridership -> Ticketing.
We must link the proven intermediate step (Ridership) to the conclusion (Ticketing).
6
Diagram Argument 5 and identify the gap
Fact: Arcadia eliminates Toll Jobs AND increases Ridership. Conclusion: Arcadia reduces Carbon. Gap: (Toll Jobs + Ridership) -> Carbon.
We must directly connect the compound factual evidence to the new conclusion.

Key Concept

Sufficient Assumptions via Formal Logic Mapping
Estimated Time:3m 30s
Question 42Question →

Legal scholar: A judicial ruling cannot be considered legally definitive unless it relies upon settled case law or explicitly overturns prior interpretive frameworks. We know that any ruling explicitly overturning prior interpretive frameworks inevitably destabilizes market expectations. The recent appellate decision regarding digital asset property rights clearly did not destabilize market expectations. Therefore, the recent appellate decision cannot be considered legally definitive.

The conclusion drawn by the legal scholar follows logically if which one of the following is assumed?

Show answer & explanation

Answer: The recent appellate decision regarding digital asset property rights did not rely upon settled case law.

Answer

The recent appellate decision regarding digital asset property rights did not rely upon settled case law.
The argument's first sentence establishes that for a ruling to be legally definitive, it must satisfy at least one of two conditions: relying on settled case law OR overturning prior frameworks. The subsequent premises establish that overturning prior frameworks always destabilizes markets, and that this specific decision did NOT destabilize markets. From this, we deduce the decision did NOT overturn prior frameworks. To conclude that the decision is definitely NOT legally definitive, we must eliminate the only other path to being definitive: relying on settled case law. The correct answer explicitly states that the decision did not rely on settled case law, perfectly closing the gap and guaranteeing the conclusion.

Step-by-Step Solution

1
Map the formal logic of the first premise.
Definitive (LD) -> Settled Case Law (SCL) OR Overturns Frameworks (OPIF). The contrapositive is: If NOT SCL AND NOT OPIF -> NOT LD.
Understanding the conditional relationship established by the word 'unless' is required to see what is necessary to prove the conclusion.
2
Map the formal logic of the second and third premises.
OPIF -> Destabilizes Market Expectations (DME). The appellate decision (AppDec) -> NOT DME.
This allows for deductions based on the specific scenario presented.
3
Derive the intermediate conclusion.
Because AppDec -> NOT DME, and OPIF -> DME, we can deduce via contrapositive that AppDec -> NOT OPIF.
Connecting the premises reveals what is already known to be true about the appellate decision.
4
Identify the logical gap to reach the final conclusion.
The final conclusion is AppDec -> NOT LD. To prove NOT LD, we need BOTH NOT SCL and NOT OPIF. We already know AppDec -> NOT OPIF. Therefore, the missing assumption is AppDec -> NOT SCL.
A sufficient assumption must perfectly bridge the gap between the derived premises and the conclusion.

Key Concept

Sufficient Assumption involving Compound Conditionals and Contrapositives
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