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Zorluk: Çok zorStatement and Conclusions or Inferences

The following clinical guidelines are extracted from the 2026 National Health Authority directive on antimicrobial stewardship.

Statement 1: A hospital is authorized to dispense a Class-X broad-spectrum antibiotic to a patient only if the patient's leukocyte count drops below 4,000 cells/mcL and the primary infection demonstrates complete resistance to all first-line therapies.
Statement 2: Despite presenting with a leukocyte count of 3,200 cells/mcL, several patients in the intensive care unit recently responded positively to a standard first-line cephalosporin treatment.

Based strictly on the clinical guidelines provided, which of the deductions below logically follow?

Conclusion I: The intensive care unit patients who responded to the cephalosporin treatment are not authorized to receive a Class-X broad-spectrum antibiotic.
Conclusion II: Any patient whose leukocyte count remains above 4,000 cells/mcL will invariably respond positively to first-line therapies.

Which of the following is the correct evaluation?

  1. Only conclusion I followsCevap
  2. B
    Only conclusion II follows
  3. C
    Both conclusion I and conclusion II follow
  4. D
    Neither conclusion I nor conclusion II follows

Cevap

Only conclusion I follows
The correct evaluation accurately applies formal logic to the administrative text. Statement 1 dictates that authorization requires BOTH a low leukocyte count AND complete resistance. By responding to a first-line cephalosporin, the patients in Statement 2 do not have complete resistance. Because they fail a necessary condition, they are strictly ineligible for the Class-X antibiotic, making Conclusion I a definitive deduction. Conclusion II is invalid because the text never establishes a causal correlation between having a high leukocyte count and being responsive to first-line therapies.

Adım Adım Çözüm

1
Analyze Statement 1 to isolate the logical conditions required for authorization.
Authorizing Class-X antibiotics requires two simultaneous necessary conditions: (1) Leukocytes < 4,000 AND (2) Complete resistance to all first-line therapies.
Identifying the formal 'only if' constraints is necessary to evaluate the validity of any subsequent deductions.
2
Evaluate the patient profile in Statement 2 against the established conditions.
The patients meet condition 1 (3,200 < 4,000) but fail condition 2 because they successfully responded to a first-line cephalosporin.
Applying the specific case facts to the general rule determines whether the required logical threshold is met.
3
Assess the validity of Conclusion I based on the findings from Step 2.
Because the patients failed to meet the second necessary condition, the contrapositive of Statement 1 strictly dictates that they cannot be authorized for Class-X antibiotics. Conclusion I definitively follows.
If any necessary condition of a conditional statement is false, the dependent outcome must also be false.
4
Assess the validity of Conclusion II by checking for unsupported correlations.
Statement 1 does not claim that failing one condition (leukocytes > 4,000) guarantees the opposite of the other condition (responding to first-line therapy). Conclusion II does not follow.
Preventing the logical fallacy of assuming independent necessary conditions are causally linked to one another.

Anahtar Kavram

Conditional Logic, Contrapositive Deductions, and the Analysis of Necessary and Sufficient Conditions
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Konular

Statement and Conclusions or Inferences

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