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Zorluk: Çok zorForming Contrapositives

Under the revised 2026 Bioethics Commission guidelines, a cognitive enhancement implant can be approved for general public distribution only if the device has been demonstrated to have zero risk of inducing memory degradation, and it either significantly improves executive function or radically accelerates neural plasticity.

Which one of the following logically follows from the guidelines above?

  1. A
    If a cognitive enhancement implant has zero risk of inducing memory degradation, and it either significantly improves executive function or radically accelerates neural plasticity, it will be approved for general public distribution.
  2. B
    If a cognitive enhancement implant is not approved for general public distribution, it must either carry some risk of inducing memory degradation, or it must neither significantly improve executive function nor radically accelerate neural plasticity.
  3. C
    If a cognitive enhancement implant carries any risk of inducing memory degradation, or if it fails to significantly improve executive function or fails to radically accelerate neural plasticity, then it cannot be approved for general public distribution.
  4. D
    If a cognitive enhancement implant carries some risk of inducing memory degradation, and it neither significantly improves executive function nor radically accelerates neural plasticity, then it cannot be approved for general public distribution.
  5. If a cognitive enhancement implant carries any risk of inducing memory degradation, or if it neither significantly improves executive function nor radically accelerates neural plasticity, it cannot be approved for general public distribution.Cevap

Cevap

The correct answer states that if an implant carries any risk of inducing memory degradation, or if it neither improves executive function nor accelerates neural plasticity, it cannot be approved.
The stimulus establishes a complex conditional relationship: Approval -> Zero Risk AND (Executive Function OR Neural Plasticity). To find what logically follows, we must find the contrapositive. According to formal logic and De Morgan's laws, we reverse the terms and negate them, flipping 'AND' to 'OR' and 'OR' to 'AND'. The negation of 'Zero Risk' is 'any risk'. The negation of the 'AND' is an 'OR'. The negation of '(Executive Function OR Neural Plasticity)' is 'neither Executive Function nor Neural Plasticity'. Putting this together creates the correct sufficient condition: 'any risk OR (neither Executive Function nor Neural Plasticity)'. This triggers the negated outcome: 'cannot be approved'. The correct option perfectly mirrors this structure.

Adım Adım Çözüm

1
Identify the sufficient and necessary conditions in the stimulus.
Sufficient (A): Approved for distribution. Necessary: Zero risk of memory degradation (Z) AND [Improves executive function (E) OR Accelerates neural plasticity (N)].
The phrase 'only if' introduces necessary conditions. Everything preceding 'only if' is the sufficient condition.
2
Symbolize the formal logic relationship.
A -> Z AND (E OR N).
Abstracting the text into logic symbols helps isolate the structure needed to form the contrapositive.
3
Form the contrapositive by negating both sides and reversing the arrow.
NOT [Z AND (E OR N)] -> NOT A.
The contrapositive is the only definitively true deduction that can be made from a universal conditional statement.
4
Apply De Morgan's laws to simplify the negated compound necessary condition.
The negation of 'Z AND (E OR N)' becomes 'NOT Z OR NOT (E OR N)'. Further applying De Morgan's to the inner condition yields 'NOT Z OR (NOT E AND NOT N)'.
De Morgan's laws dictate that when negating a compound statement, 'AND' changes to 'OR', and 'OR' changes to 'AND'.
5
Translate the simplified logical contrapositive back into English.
If an implant does not have zero risk (has ANY risk), OR if it lacks both benefits (NEITHER significantly improves E NOR radically accelerates N), then it cannot be approved (NOT A).
This translation matches the correct answer choice perfectly.

Anahtar Kavram

Forming complex contrapositives using De Morgan's laws
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Konular

Forming Contrapositives

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