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Zorluk: OrtaMust Be True / Most Strongly Supported

Materials scientists evaluating marine protective treatments established the following facts regarding commercial hull applications:

• Any protective coating that incorporates fluoropolymer matrix F resists barnacle adhesion in saltwater environments.
• Every coating that resists barnacle adhesion in saltwater environments also prevents hull corrosion, provided the coating is applied at temperatures of at least 15°C.
• Whenever a coating prevents hull corrosion and the vessel receives bi-monthly freshwater washings, the vessel's scheduled drydock interval is extended beyond five years.
• Coating Z incorporates fluoropolymer matrix F, was applied to a commercial cargo vessel at a surface temperature of 21°C, and the vessel receives bi-monthly freshwater washings.

If the statements above are true, which one of the following must be true based on them?

  1. A
    Any commercial coating that successfully extends a vessel's scheduled drydock interval beyond five years incorporates fluoropolymer matrix F.
  2. B
    If Coating Z had been applied at a temperature below 15°C, it would have failed to resist barnacle adhesion in saltwater environments.
  3. The scheduled drydock interval for the commercial cargo vessel treated with Coating Z is extended beyond five years.Cevap
  4. D
    Resisting barnacle adhesion in saltwater environments is a necessary requirement for a coating to incorporate fluoropolymer matrix F.
  5. E
    Coating Z will prevent hull corrosion on any vessel even if that vessel never receives bi-monthly freshwater washings.

Cevap

The scheduled drydock interval for the commercial cargo vessel treated with Coating Z is extended beyond five years.
The conclusion that the drydock interval is extended beyond five years is fully derived through a complete chain of valid deductive steps: Coating Z incorporates fluoropolymer matrix F (ensuring barnacle resistance), was applied at 21°C (ensuring corrosion prevention), and receives bi-monthly freshwater washings (guaranteeing the extended drydock interval).

Adım Adım Çözüm

1
Map the conditional statements provided in the stimulus
(1) Fluoropolymer matrix F → Resists barnacle adhesion; (2) Resists barnacle adhesion + Applied at ≥ 15°C → Prevents hull corrosion; (3) Prevents hull corrosion + Bi-monthly washings → Drydock interval > 5 years.
Establishing explicit conditional chains allows for systematic deductive evaluation.
2
Apply the specific factual premises regarding Coating Z to the first two links of the chain
Coating Z has fluoropolymer matrix F, so it resists barnacle adhesion. Since it was applied at 21°C (which satisfies the ≥ 15°C threshold), Coating Z definitely prevents hull corrosion.
Testing the initial conditions verifies that the intermediate conclusion is soundly triggered.
3
Evaluate the final conditional link
Because Coating Z prevents hull corrosion and the vessel receives bi-monthly freshwater washings, the final necessary outcome is triggered: the scheduled drydock interval is extended beyond five years.
Completing the deduction identifies the statement that is logically guaranteed.

Anahtar Kavram

Deductive Conditional Chaining and Modus Ponens
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Konular

Must Be True / Most Strongly Supported

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