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Difficulty: MediumNecessary vs. Sufficient Condition Flaws

In logical reasoning, arguments often fail by misinterpreting conditional relationships, specifically by treating a condition that is necessary for an outcome as if it were sufficient to guarantee that outcome (or vice versa). Which of the following arguments commit this logical flaw? (Select all that apply)

  1. Anyone who is a professionally certified diver has completed over 50 hours of open-water training. Mark has completed 60 hours of open-water training. Therefore, Mark must be a professionally certified diver.Answer
  2. B
    Data consistently indicates that individuals who consume green tea daily live longer on average than those who do not. Hence, the antioxidants in green tea are responsible for extending human lifespan.
  3. C
    A novel will be considered for the literary award only if it was published in the current calendar year. The novel Echoes of Time was published three years ago. Thus, it will not be considered for the award.
  4. A thriving botanical garden requires nutrient-rich soil. The city's new community garden is not thriving, which means its soil must not be nutrient-rich.Answer
  5. E
    Every structural beam in the new suspension bridge is manufactured from an incredibly lightweight alloy. Consequently, the assembled bridge as a whole must be incredibly lightweight.

Answer

The correct choices are the argument regarding the certified diver and the argument regarding the botanical garden.
The correct choices both fail to distinguish between sufficient and necessary conditions. The argument about the certified diver commits an Illegal Reversal by assuming that meeting the necessary training hours guarantees certification. The argument about the botanical garden commits an Illegal Negation by assuming that because a sufficient condition (thriving) is absent, the necessary condition (nutrient-rich soil) must also be absent. In logic, an Illegal Negation fundamentally relies on the same misunderstanding of conditionality as an Illegal Reversal.

Step-by-Step Solution

1
Analyze each argument to extract its structural logic and identify its core premise and conclusion.
Arguments are mapped into conditional, causal, or part-to-whole frameworks.
Identifying the structure is required to evaluate the validity of the reasoning.
2
Identify arguments that mistakenly invert the relationship between sufficient and necessary conditions.
The diver argument demonstrates an Illegal Reversal, and the botanical garden argument demonstrates an Illegal Negation.
Both of these flaws fundamentally mistake a necessary condition for a sufficient one (or vice versa), matching the prompt's criteria.
3
Eliminate arguments that exhibit other flaws or are logically valid.
The green tea argument is a causal flaw, the suspension bridge argument is a composition flaw, and the literary award argument is a valid contrapositive.
Only options containing conditional logic flaws fit the precise requirement of the question stem.

Key Concept

Distinguishing between conditions that guarantee an outcome (sufficient) and conditions that are merely required for an outcome (necessary).
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Necessary vs. Sufficient Condition Flaws

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