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Zorluk: OrtaMust Be True Questions

According to recent climatological models regarding atmospheric disturbances:

Every equatorial atmospheric disturbance that reaches category 3 intensity causes significant coastal erosion on the eastern seaboard. Most equatorial atmospheric disturbances that reach category 3 intensity are accompanied by a rapid pressure drop. Any weather system accompanied by a rapid pressure drop triggers localized cooling in the upper troposphere. Furthermore, no weather system that triggers localized cooling in the upper troposphere dissipates within 48 hours of formation.

Based on the climatological models above, which of the following statements must be true? Select all that apply.

  1. At least some weather systems that cause significant coastal erosion on the eastern seaboard do not dissipate within 48 hours of formation.Cevap
  2. At least some equatorial atmospheric disturbances that reach category 3 intensity trigger localized cooling in the upper troposphere.Cevap
  3. C
    Any weather system accompanied by a rapid pressure drop causes significant coastal erosion on the eastern seaboard.
  4. D
    Any weather system that does not trigger localized cooling in the upper troposphere dissipates within 48 hours of formation.
  5. E
    Every equatorial atmospheric disturbance that reaches category 3 intensity triggers localized cooling in the upper troposphere.

Cevap

The statements that must be true are that some weather systems causing coastal erosion do not dissipate within 48 hours, and that some category 3 equatorial atmospheric disturbances trigger localized cooling.
Based on the logical chain, most category 3 disturbances cause a pressure drop, which causes cooling, which prevents dissipation within 48 hours. Since all of these disturbances also cause coastal erosion, there is a guaranteed overlap between systems that cause erosion and systems that do not dissipate quickly. Additionally, the chain directly proves that at least some (in fact, most) of these disturbances trigger localized cooling.

Adım Adım Çözüm

1
Map the conditional statements provided in the stimulus.
All EAD3 -> CE; Most EAD3 -> RPD; All RPD -> LC; All LC -> NOT D48.
Formalizing the logic makes it easier to combine terms and identify valid inferences.
2
Chain the absolute conditional statements together.
Since All RPD -> LC and All LC -> NOT D48, we can deduce that All RPD -> NOT D48.
Transitive logic allows combining sequential conditional rules.
3
Integrate the 'most' quantifier into the absolute chain.
Because Most EAD3 -> RPD, and All RPD -> LC -> NOT D48, we can infer that Most EAD3 -> LC, and Most EAD3 -> NOT D48.
A 'most' statement can be extended by an 'all' statement that follows its necessary condition.
4
Evaluate overlaps to find valid 'some' inferences.
All EAD3 -> CE, and Most EAD3 -> NOT D48. Because a single group (EAD3) entirely possesses one trait and mostly possesses another, those traits must overlap. Therefore, Some CE -> NOT D48.
If all A are B, and most A are C, then at least some B must be C.

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Must Be True / Formal Logic Deductions
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