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Difficulty: MediumApplying the Negation Technique

Economist: The government's new vocational initiative provides displaced manufacturing workers with training in advanced software engineering. Proponents argue this will drastically reduce unemployment within this demographic. However, mastering advanced software engineering requires a strong foundation in discrete mathematics, a background that the vast majority of displaced manufacturing workers currently lack. Therefore, because of this educational deficit, the initiative will fail to significantly reduce unemployment among these workers.

Which one of the following is an assumption required by the economist's argument?

  1. A
    Displaced manufacturing workers would be unable to learn discrete mathematics even if the initiative provided such instruction.
  2. B
    Not a single displaced manufacturing worker targeted by the initiative currently possesses a strong foundation in discrete mathematics.
  3. C
    Tech companies generally refuse to hire software engineers whose primary work experience is in manufacturing.
  4. The government's vocational initiative does not provide instruction in discrete mathematics alongside its software engineering training.Answer
  5. E
    Advanced software engineering is the only field with enough job openings to significantly reduce unemployment among these workers.

Answer

The government's vocational initiative does not provide instruction in discrete mathematics alongside its software engineering training.
This is a necessary assumption because it bridges the gap between the workers' current lack of knowledge and the program's ultimate failure. To prove this, we apply the Negation Technique: 'The vocational initiative DOES provide instruction in discrete mathematics alongside its software engineering training.' If the program provides this math instruction, the workers' current educational deficit is actively solved by the program itself. This completely destroys the economist's conclusion that the program will fail 'because of this educational deficit'. Therefore, assuming the program does not teach the math is logically required for the argument to survive.

Step-by-Step Solution

1
Analyze the core structure of the argument, isolating the premises from the main conclusion.
Premise: Workers currently lack discrete math, which is required for advanced software engineering. Conclusion: The program will fail because of this educational deficit.
Identifying the exact basis for the conclusion helps pinpoint the logical gap the author has left open.
2
Identify the logical gap between the evidence provided and the absolute claim made in the conclusion.
The economist assumes that because the workers *currently* lack the math background, this deficit will permanently prevent them from learning the software engineering material during the program.
An assumption is an unstated premise that bridges the gap between the evidence and the conclusion.
3
Evaluate the answer choices using the Negation Technique to determine which one is strictly required.
Negating the correct option yields: 'The initiative DOES provide instruction in discrete mathematics.' If true, the current deficit is solved by the program itself, destroying the argument's conclusion.
The Negation Technique definitively separates necessary assumptions (whose negation destroys the argument) from attractive distractors.

Key Concept

Applying the Negation Technique to Necessary Assumptions
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Topics

Applying the Negation Technique

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