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Zorluk: OrtaIdentifying Must-Be-True Statements and Valid Deductions

Under the 2026 Municipal Clean Power Accord, any regional microgrid that sources more than 60 percent of its electricity from solar energy must maintain a battery storage reserve capable of supplying at least 4 hours of continuous power, unless it uses hydro-pumped storage as its primary backup reserve. Every microgrid operating in District 7 sources at least 75 percent of its electricity from solar energy. Microgrid Alpha is located in District 7 and does not maintain a battery storage reserve capable of supplying at least 4 hours of continuous power.

If the statements above are true, which of the following must also be true about Microgrid Alpha?

  1. A
    Microgrid Alpha sources a higher percentage of its electricity from solar energy than any other microgrid in District 7.
  2. B
    Microgrid Alpha fails to comply with the regulatory guidelines established under the 2026 Municipal Clean Power Accord.
  3. Microgrid Alpha uses hydro-pumped storage as its primary backup reserve.Cevap
  4. D
    If a microgrid in District 7 uses hydro-pumped storage as its primary backup reserve, it sources less than 60 percent of its electricity from solar energy.
  5. E
    Microgrid Alpha maintains a battery storage reserve capable of supplying power for fewer than 3 hours.

Cevap

Microgrid Alpha uses hydro-pumped storage as its primary backup reserve.
The passage establishes that any microgrid sourcing over 60% solar power must maintain a battery reserve of at least 4 hours, UNLESS it uses hydro-pumped storage as its primary backup reserve. Microgrid Alpha is in District 7, meaning its solar sourcing is at least 75% (which is strictly greater than 60%). However, Microgrid Alpha does not maintain the 4-hour battery reserve. To remain consistent with the factual premises, Microgrid Alpha must fall under the exception clause. Therefore, it MUST use hydro-pumped storage as its primary backup reserve.

Adım Adım Çözüm

1
Identify the given conditional rules and factual premises.
Rule: If Solar > 60% AND NOT (Hydro-Pumped Storage) → Must have Battery Reserve ≥ 4 hours. Fact 1: District 7 microgrids have Solar ≥ 75%. Fact 2: Microgrid Alpha is in District 7, so its Solar ≥ 75% (> 60%). Fact 3: Microgrid Alpha does NOT have Battery Reserve ≥ 4 hours.
Establishing formal logical relationships allows for precise deduction.
2
Apply Modus Tollens (contrapositive reasoning) to the conditional rule.
Since Microgrid Alpha satisfies the condition (Solar > 60%) but fails to satisfy the requirement (Battery Reserve ≥ 4 hours), it must satisfy the exemption clause.
If a required consequence is absent for a subject that meets the trigger condition, the exemption condition must hold true.
3
Deduce the necessary truth regarding Microgrid Alpha.
Microgrid Alpha must use hydro-pumped storage as its primary backup reserve.
This is the only logically guaranteed outcome that prevents a contradiction with the provided premises.

Anahtar Kavram

Conditional Logic Contrapositive and Valid Deductions
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Konular

Identifying Must-Be-True Statements and Valid Deductions

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