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Zorluk: ZorChaining Conditional Statements

A national health ministry is establishing new regulatory standards for clinical trials. The regulations are governed by the following conditional rules:

- Any trial that tests a novel medical device must undergo a rigorous safety audit.
- A rigorous safety audit is conducted only if the trial employs an independent oversight committee.
- If a trial employs an independent oversight committee, then it must allocate five percent of its budget to patient advocacy.
- A trial cannot employ an independent oversight committee if it is exclusively sponsored by a for-profit pharmaceutical company.
- Unless a trial allocates five percent of its budget to patient advocacy, it cannot qualify for the federal innovation grant.
- All trials that are exclusively sponsored by a for-profit pharmaceutical company must undergo a commercial viability review.

Match each proposed clinical trial profile below with the deductive inference that must logically follow from the regulations.

  • A trial that tests a novel medical deviceMust employ an independent oversight committee and allocate five percent of its budget to patient advocacy
  • A trial exclusively sponsored by a for-profit pharmaceutical companyMust undergo a commercial viability review and cannot test a novel medical device
  • A trial that qualifies for the federal innovation grant but does not employ an independent oversight committeeMust allocate five percent of its budget to patient advocacy and cannot undergo a rigorous safety audit
  • A trial that fails to allocate five percent of its budget to patient advocacyCannot qualify for the federal innovation grant and cannot test a novel medical device

Cevap

The correct matches pair each trial profile with its necessary deductive inferences: 1) Testing a novel medical device pairs with employing an oversight committee and allocating budget to patient advocacy. 2) For-profit sponsorship pairs with undergoing a commercial viability review and being unable to test a novel device. 3) Qualifying for the federal grant without an oversight committee pairs with allocating budget to patient advocacy and avoiding a rigorous safety audit. 4) Failing to allocate budget to patient advocacy pairs with being unable to qualify for the federal grant and unable to test a novel medical device.
Each correct match is derived by applying the rules of formal logic—specifically transitive chaining and contrapositives—to the conditional regulations provided. Testing a novel device triggers a chain reaction leading to patient advocacy funding. Corporate sponsorship forbids the oversight committee, which backwards-chains to forbid testing a novel device. The federal grant requires patient advocacy, while lacking an oversight committee backwards-chains to forbid the safety audit. Failing to fund patient advocacy backwards-chains to eliminate the federal grant and all prerequisites leading up to patient advocacy.

Adım Adım Çözüm

1
Translate the regulatory rules into formal conditional statements using abbreviations.
Let ND = novel device, RSA = rigorous safety audit, IOC = independent oversight committee, PA = patient advocacy, FPC = for-profit pharmaceutical company, FIG = federal innovation grant, CVR = commercial viability review.
Rule 1: ND -> RSA
Rule 2: RSA -> IOC
Rule 3: IOC -> PA
Rule 4: FPC -> ~IOC
Rule 5: FIG -> PA (translated from 'Unless PA, ~FIG')
Rule 6: FPC -> CVR
Converting natural language with complex indicators ('only if', 'unless', 'cannot... if') into formal logic simplifies the deduction process and exposes transitive relationships.
2
Combine the conditional statements into logical chains.
Core Chain: ND -> RSA -> IOC -> PA
Branch 1: FPC -> ~IOC and FPC -> CVR
Branch 2: FIG -> PA
Contrapositive of Core Chain: ~PA -> ~IOC -> ~RSA -> ~ND
Connecting overlapping necessary and sufficient conditions creates the deductive pathways required to solve the question.
3
Analyze each trial profile against the established chains to identify the necessary inferences.
Profile 1 (ND): Following the Core Chain, ND guarantees RSA, IOC, and PA.
Profile 2 (FPC): FPC guarantees CVR, and triggers ~IOC. Through the contrapositive chain, ~IOC -> ~RSA -> ~ND.
Profile 3 (FIG and ~IOC): FIG guarantees PA. The condition ~IOC triggers the contrapositive ~IOC -> ~RSA -> ~ND. Thus, PA and ~RSA are deduced.
Profile 4 (~PA): Taking the contrapositive of Branch 2, ~PA -> ~FIG. Through the contrapositive of the Core Chain, ~PA -> ~IOC -> ~RSA -> ~ND. Thus, ~FIG and ~ND are deduced.
Matching the given conditions in the profiles to the beginning of the logical chains reveals all downstream deductions.

Anahtar Kavram

Chaining Conditional Statements and Contrapositives
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Konular

Chaining Conditional Statements

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