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Difficulty: MediumIdentifying Sufficient Assumptions

If agricultural yields are to be sustained over the next century, topsoil erosion must be drastically reduced. Drastically reducing topsoil erosion requires the widespread adoption of no-till farming techniques. The government’s new agricultural subsidy program will ensure the widespread adoption of these no-till techniques. Therefore, the new subsidy program will guarantee that agricultural yields are sustained over the next century.

Which one of the following, if assumed, enables the conclusion to be properly drawn?

  1. The widespread adoption of no-till farming techniques is sufficient to guarantee that agricultural yields are sustained over the next century.Answer
  2. B
    If agricultural yields are sustained over the next century, then the widespread adoption of no-till farming techniques must have successfully occurred.
  3. C
    Agricultural programs that fail to ensure the widespread adoption of no-till farming techniques cannot successfully sustain agricultural yields over the next century.
  4. D
    The government's new agricultural subsidy program is the only feasible policy for drastically reducing topsoil erosion in the near future.
  5. E
    Most agricultural programs that result in the widespread adoption of no-till farming techniques also succeed in sustaining agricultural yields over the next century.

Answer

The statement that the widespread adoption of no-till farming techniques is sufficient to guarantee that agricultural yields are sustained.
The correct answer provides the exact logical bridge needed to complete the argument's chain. The premises establish that the subsidy program will lead to no-till farming. By adding the assumption that no-till farming guarantees sustained agricultural yields, the conclusion (that the subsidy program guarantees sustained yields) is mathematically forced to be true.

Step-by-Step Solution

1
Map the conditional logic of the premises.
Premise 1: Sustained Yields -> Reduce Erosion. Premise 2: Reduce Erosion -> No-Till Farming. Premise 3: Subsidy Program -> No-Till Farming.
To identify the structural elements the author provides to build the argument.
2
Identify the conclusion and compare it to the premises.
Conclusion: Subsidy Program -> Sustained Yields. The premises only establish that the Subsidy Program leads to No-Till Farming.
To pinpoint the exact logical leap the author makes.
3
Determine the missing link required to justify the conclusion.
The argument needs a rule connecting the result of the program (No-Till Farming) to the desired outcome (Sustained Yields). The missing link is: No-Till Farming -> Sustained Yields.
Because if No-Till Farming guarantees Sustained Yields, the chain (Subsidy Program -> No-Till Farming -> Sustained Yields) is complete and valid.

Key Concept

Identifying Sufficient Assumptions in Formal Logic Chains
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Topics

Identifying Sufficient Assumptions

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