Examkin

Soru

Zorluk: ZorStatement and Conclusions or Inferences

Evaluate the following statements derived from a state health department audit, and determine which of the subsequent conclusions logically follow(s).

Statements:
1. Every public hospital that successfully reduced emergency room wait times by 30% this quarter adopted the Triage-Plus protocol.
2. Some public hospitals facing severe budget deficits adopted the Triage-Plus protocol.
3. No facility that adopted the Triage-Plus protocol experienced an increase in patient mortality rates.

Conclusions:
I. A public hospital that experienced an increase in patient mortality rates did not successfully reduce its emergency room wait times by 30% this quarter.
II. Any public hospital that failed to adopt the Triage-Plus protocol experienced an increase in patient mortality rates.

Based on the information above, which of the options is correct?

  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
Conclusion I is a valid logical deduction. By chaining Statement 1 (reducing wait times implies adopting the protocol) and Statement 3 (adopting the protocol implies no mortality increase), we conclude that reducing wait times implies no mortality increase. The contrapositive states that if there IS a mortality increase, wait times were NOT reduced, which exactly matches Conclusion I. Conclusion II is invalid because it assumes the inverse of Statement 3; knowing what happens when a protocol is adopted does not dictate what happens when it is not.

Adım Adım Çözüm

1
Translate the statements into logical relationships to track conditions objectively.
Statement 1: Reduced Wait Times → Adopted Protocol. Statement 2: Some Deficit Hospitals → Adopted Protocol. Statement 3: Adopted Protocol → NO Increase in Mortality.
Formalizing the logic prevents misinterpretation based on external assumptions.
2
Evaluate Conclusion I by combining relevant statements.
Since 'Reduced Wait Times' requires 'Adopted Protocol', and 'Adopted Protocol' guarantees 'NO Increase in Mortality', we deduce: 'Reduced Wait Times → NO Increase in Mortality'. The contrapositive of this deduction is 'Increase in Mortality → NOT Reduced Wait Times'.
A logical conditional statement and its contrapositive are always mathematically equivalent. Conclusion I perfectly matches this contrapositive, making it valid.
3
Evaluate Conclusion II using formal logic rules.
Statement 3 establishes 'Adopted Protocol → NO Increase in Mortality'. Conclusion II claims 'NOT Adopted Protocol → Increase in Mortality'. This is the inverse of Statement 3, not the contrapositive.
The inverse of a true statement is not necessarily true. We cannot logically infer what happens to mortality rates if the protocol is not adopted. Therefore, Conclusion II is invalid.

Anahtar Kavram

Statement and Conclusions or Inferences
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Konular

Statement and Conclusions or Inferences

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