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

Every commercial flight route operating out of Hub H that utilizes wide-body aircraft is assigned a Tier-1 maintenance protocol. Any route at Hub H assigned a Tier-1 maintenance protocol is subjected to mandatory weekly safety audits unless that route serves exclusively international destinations. Last year, every route at Hub H subjected to mandatory weekly safety audits was operated by FlightCorp, and FlightCorp operated no routes at Hub H that served international destinations.

If the statements above are true, which of the following must also be true about Hub H last year?

  1. A
    Every route at Hub H operated by FlightCorp utilized wide-body aircraft.
  2. B
    FlightCorp operated more domestic routes out of Hub H than did any other airline.
  3. Any route at Hub H that utilized wide-body aircraft but was not operated by FlightCorp served exclusively international destinations.Cevap
  4. D
    Any route at Hub H that served exclusively international destinations was assigned a Tier-1 maintenance protocol.
  5. E
    No route at Hub H serving exclusively international destinations was subjected to mandatory weekly safety audits.

Cevap

Any route at Hub H that utilized wide-body aircraft but was not operated by FlightCorp served exclusively international destinations.
The statement regarding wide-body routes not operated by FlightCorp must be true based on the logical structure of the premises: Wide-body aircraft routes automatically receive Tier-1 maintenance. Tier-1 routes require weekly audits unless they are exclusively international. Because all audited routes were operated by FlightCorp, any non-FlightCorp route was not audited. For a Tier-1 route to avoid weekly audits, it must meet the exemption condition of serving exclusively international destinations.

Adım Adım Çözüm

1
Represent the premises as conditional logic statements.
1. Wide-Body -> Tier-1 Maintenance.
2. Tier-1 Maintenance AND NOT Exclusively International -> Weekly Audits.
3. Weekly Audits -> Operated by FlightCorp.
Establishing clear conditional rules allows logical synthesis.
2
Take the contrapositive of Premise 3.
NOT Operated by FlightCorp -> NOT Weekly Audits.
If a route was not operated by FlightCorp, it could not have been subjected to mandatory weekly safety audits.
3
Combine the premises for a route that uses wide-body aircraft but is not operated by FlightCorp.
The route has Tier-1 Maintenance (from Premise 1) and does NOT undergo Weekly Audits (from contrapositive of Premise 3).
Linking the conditions isolates the exception clause in Premise 2.
4
Apply Premise 2 to the combined state.
Premise 2 states that Tier-1 routes undergo weekly audits UNLESS they serve exclusively international destinations. Since this route has Tier-1 maintenance but does NOT undergo weekly audits, it MUST fall under the exception and serve exclusively international destinations.
The absence of the audit requirement for a Tier-1 route strictly necessitates that the exemption condition (exclusively international) holds true.

Anahtar Kavram

Conditional Logic Deductions and Contrapositives
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Konular

Identifying Must-Be-True Statements and Valid Deductions

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