Examkin

Question

Difficulty: Very hardConditional Logic and Formal Deductions

A biomedical research consortium establishes the following funding protocol: A clinical study receives financial backing only if the project team secures institutional ethics board certification and implements synthetic biomarker tracking. Securing institutional ethics board certification requires that the study protocol either undergoes double-blind peer review or obtains a regulatory exemption from the central health committee.

Consider the following assertion: If Study X was denied financial backing and did not obtain a regulatory exemption from the central health committee, then Study X must have failed to undergo double-blind peer review.

Answer: Answer

Answer

The statement is False.
Evaluating the statement as False is correct because the rules state that financial backing requires ethics certification. The absence of financial backing does not imply that ethics certification was withheld or that double-blind peer review did not occur; Study X could have fulfilled the peer review requirement but missed financial backing due to another missing requirement (such as synthetic biomarker tracking).

Step-by-Step Solution

1
Formalize the conditional premises from the protocol.
Premise 1: Financial Backing → (Ethics Certification AND Synthetic Biomarker Tracking).
Premise 2: Ethics Certification → (Double-Blind Peer Review OR Regulatory Exemption).
Establishing formal logic notation prevents misinterpreting necessary conditions as sufficient conditions.
2
Analyze the given facts about Study X.
Facts: ¬Financial Backing and ¬Regulatory Exemption.
Identify which components of the conditional statements are known to be true or false.
3
Test the validity of the deduction: ¬Financial Backing → ¬Double-Blind Peer Review.
From Premise 1, Financial Backing requires Ethics Certification. However, the absence of Financial Backing (¬Financial Backing) does not logically imply the absence of Ethics Certification (¬Ethics Certification).
Denying the antecedent (¬Financial Backing) yields no valid inference about the consequent (Ethics Certification).
4
Determine whether double-blind peer review must be false.
Since Ethics Certification could still be true, Double-Blind Peer Review could also be true. Therefore, it is not logically necessary that Study X failed to undergo double-blind peer review.
A statement is only logically necessary if it must be true in all possible valid scenarios consistent with the premises.

Key Concept

Conditional Logic: Distinguishing Necessary vs. Sufficient Conditions and Avoiding the Mistaken Negation Fallacy
Rate this question

Topics

Conditional Logic and Formal Deductions

More questions from this topic