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Zorluk: Çok zorForming Contrapositives

According to the newly established directives by the Orbital Commerce Commission, a commercial satellite launch qualifies for priority scheduling only if the launching corporation submits a comprehensive debris mitigation plan and at least one of the following occurs: the payload serves a registered humanitarian function, or an independent aerospace auditor certifies the vehicle's structural integrity.

Which of the following statements must be logically true based on the directives above?

  1. A
    If a launching corporation fails to submit a comprehensive debris mitigation plan, or if the payload does not serve a registered humanitarian function, or if an independent aerospace auditor fails to certify the vehicle's structural integrity, then the commercial satellite launch will not qualify for priority scheduling.
  2. B
    If a launching corporation submits a comprehensive debris mitigation plan and at least one of the following occurs—the payload serves a registered humanitarian function or an independent aerospace auditor certifies the vehicle's structural integrity—then the commercial satellite launch will qualify for priority scheduling.
  3. C
    If a launching corporation submits a comprehensive debris mitigation plan, but the payload does not serve a registered humanitarian function, then the commercial satellite launch will not qualify for priority scheduling.
  4. If a launching corporation fails to submit a comprehensive debris mitigation plan, or if both the payload does not serve a registered humanitarian function and an independent aerospace auditor fails to certify the vehicle's structural integrity, then the commercial satellite launch will not qualify for priority scheduling.Cevap
  5. E
    If a commercial satellite launch does not qualify for priority scheduling, it must be the case that the launching corporation failed to submit a comprehensive debris mitigation plan, or both the payload did not serve a registered humanitarian function and an independent aerospace auditor failed to certify the vehicle's structural integrity.

Cevap

If a launching corporation fails to submit a comprehensive debris mitigation plan, or if both the payload does not serve a registered humanitarian function and an independent aerospace auditor fails to certify the vehicle's structural integrity, then the commercial satellite launch will not qualify for priority scheduling.
The correct answer accurately applies the contrapositive to a compound conditional. The stimulus dictates that for a launch to qualify, it needs a mitigation plan AND at least one of two other factors (humanitarian function OR auditor certification). If it lacks the mitigation plan, it fails. Alternatively, if it lacks BOTH of the other factors, it fails. The correct choice perfectly captures this dynamic.

Adım Adım Çözüm

1
Deconstruct the stimulus into formal conditional logic.
Priority Scheduling (P) → Mitigation Plan (M) AND [Humanitarian Function (H) OR Auditor Certification (A)].
Accurately representing the necessary conditions is required before attempting to find the contrapositive.
2
Apply the process of forming a contrapositive by reversing and negating the terms.
NOT {Mitigation Plan (M) AND [Humanitarian Function (H) OR Auditor Certification (A)]} → NOT Priority Scheduling (P).
The logically valid inference from any conditional statement is its contrapositive.
3
Apply De Morgan's laws to properly negate the compound necessary condition.
The negation of 'M AND (H OR A)' becomes 'NOT M OR NOT (H OR A)'. Applying De Morgan's again to the inner bracket yields 'NOT M OR (NOT H AND NOT A)'.
Negating an 'AND' requires switching it to an 'OR', and negating an 'OR' requires switching it to an 'AND'.
4
Translate the final logical notation back into natural language.
If the corporation does not submit a plan (NOT M), OR if the payload lacks a humanitarian function AND the auditor fails to certify (NOT H AND NOT A), then the launch does not get priority scheduling (NOT P).
The correct answer choice will mirror this exact logical relationship without confusing necessary and sufficient conditions.

Anahtar Kavram

Forming contrapositives of compound conditional statements using De Morgan's laws.
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Konular

Forming Contrapositives

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