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Difficulty: MediumNecessary vs. Sufficient Condition Flaws

Which of the following arguments contain a reasoning flaw that arises specifically from confusing a necessary condition with a sufficient condition? Select all that apply.

  1. A thriving coral reef ecosystem always contains a diverse population of symbiotic algae. The reef off the coast of San Marcos contains a diverse population of symbiotic algae, which means it must be a thriving coral reef ecosystem.Answer
  2. B
    A software application is immune to the new malware only if it was patched in the last 24 hours. The legacy inventory system was not patched in the last 24 hours, so it cannot be immune to the malware.
  3. If a municipality increases its public transportation budget, downtown traffic congestion will decrease. The city council decided against increasing the public transportation budget, so downtown traffic congestion will not decrease.Answer
  4. D
    Recent data shows a strong association between consuming fermented foods and a lower incidence of inflammatory diseases. Clearly, consuming fermented foods actively reduces systemic inflammation.
  5. E
    The marketing division saw a 20 percent budget increase this year, while the research division saw only a 10 percent increase. It is evident that the marketing division received a larger absolute increase in funding than the research division.

Answer

The argument about the coral reef ecosystem (which commits an illegal reversal) and the argument about the public transportation budget (which commits an illegal negation).
The correct arguments demonstrate the two primary ways to confuse necessary and sufficient conditions. The coral reef argument illustrates an illegal reversal by assuming that meeting a necessary requirement (having diverse algae) is sufficient to guarantee the outcome. The public transportation argument illustrates an illegal negation by assuming that failing to meet a sufficient condition (increasing the budget) guarantees that the outcome (decreased congestion) will not occur.

Step-by-Step Solution

1
Identify the logical flaw requested in the question stem.
The target flaw is confusing a necessary condition with a sufficient condition, which manifests as either an illegal reversal (A -> B; therefore B -> A) or an illegal negation (A -> B; therefore ~A -> ~B).
Understanding the exact structural nature of the target flaw is required to evaluate each option.
2
Evaluate the conditional structure of the coral reef ecosystem argument.
Premise: Thriving -> Diverse Algae. Conclusion: Diverse Algae -> Thriving. This is an illegal reversal, which perfectly matches the target flaw.
This determines that the coral reef argument is one of the correct answers.
3
Evaluate the conditional structure of the software application argument.
Premise: Immune -> Patched. Conclusion: ~Patched -> ~Immune. This is a valid application of the contrapositive. There is no logical flaw.
This rules out the software application argument as it is structurally valid.
4
Evaluate the conditional structure of the public transportation argument.
Premise: Increased Budget -> Decreased Congestion. Conclusion: ~Increased Budget -> ~Decreased Congestion. This is an illegal negation, matching the target flaw.
This determines that the public transportation argument is the second correct answer.
5
Analyze the remaining two arguments to confirm they do not contain the target flaw.
The fermented foods argument contains a correlation-to-causation fallacy. The budget division argument confuses percentages with absolute numbers. Neither commits a conditional flaw.
This confirms that no other options should be selected.

Key Concept

Identifying conditional reasoning flaws, specifically illegal reversals and illegal negations, where sufficient and necessary conditions are improperly interchanged.
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Topics

Necessary vs. Sufficient Condition Flaws

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