Question

Difficulty: EasyNecessary vs. Sufficient Condition Flaws

Match each logical argument scenario below with the correct description of its reasoning structure or logical flaw.

  • To be a professional chef, one must have excellent knife skills. David has excellent knife skills, so he will undoubtedly become a professional chef.Treats a condition that is required for a certain status as though it were enough to guarantee that status.
  • If a company offers a high salary, it will attract top talent. TechCorp does not offer a high salary, so it will not attract top talent.Assumes that the absence of a condition that ensures an outcome will necessarily result in the absence of that outcome.
  • A building can pass inspection only if its wiring is up to code. The old library's wiring is not up to code, so it will not pass inspection.Correctly deduces that the absence of a required condition guarantees the absence of the associated outcome.
  • Every student who completes the extra credit will pass the class. Emma completed the extra credit, so she will pass the class.Correctly concludes that if a condition is sufficient to produce an outcome, the presence of that condition ensures the outcome.

Answer

The professional chef scenario matches 'Treats a condition that is required...'; the company salary scenario matches 'Assumes that the absence of a condition...'; the building inspection scenario matches 'Correctly deduces that the absence...'; and the extra credit scenario matches 'Correctly concludes that if a condition is sufficient...'.
Each scenario maps to its precise logical structure. The first two scenarios illustrate the classic conditional flaws of Illegal Reversal and Illegal Negation, respectively, while the latter two scenarios successfully execute valid conditional inferences without flaw.

Step-by-Step Solution

1
Analyze the first scenario about the professional chef.
Identify that the argument takes a necessary condition (excellent knife skills) and incorrectly assumes it is sufficient to guarantee becoming a chef.
This establishes the 'Illegal Reversal' flaw.
2
Analyze the second scenario about the company salary.
Identify that the argument takes a sufficient condition (high salary) and incorrectly assumes its absence guarantees the absence of the result.
This establishes the 'Illegal Negation' flaw.
3
Analyze the third scenario about building inspection.
Identify that 'only if' introduces a necessary condition. The argument correctly deduces that failing the necessary condition means failing the outcome.
This demonstrates valid contrapositive reasoning.
4
Analyze the fourth scenario about extra credit.
Identify that 'Every student who' introduces a sufficient condition. The argument correctly concludes the outcome will occur because the condition is met.
This demonstrates valid conditional reasoning.

Key Concept

Distinguishing valid conditional inferences from necessary vs. sufficient condition flaws (Illegal Reversal and Illegal Negation).
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