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If a tectonic plate subducts at an angle greater than 45 degrees, the resulting volcanic arc is invariably situated more than 200 kilometers from the corresponding oceanic trench. Furthermore, no volcanic arc situated more than 200 kilometers from a trench produces tholeiitic basalt exclusively. However, geological surveys have confirmed that most volcanic arcs within the Cenozoic Belt produce tholeiitic basalt exclusively.

Which one of the following statements can be properly inferred from the information above?

  1. A
    If a volcanic arc does not produce tholeiitic basalt exclusively, it was formed by a tectonic plate subducting at an angle greater than 45 degrees.
  2. B
    None of the volcanic arcs within the Cenozoic Belt are situated more than 200 kilometers from their corresponding oceanic trench.
  3. Most volcanic arcs within the Cenozoic Belt are the result of tectonic plates subducting at an angle of 45 degrees or less.Cevap
  4. D
    Any volcanic arc situated 200 kilometers or less from a trench will invariably produce tholeiitic basalt exclusively.
  5. E
    The subduction angle of a tectonic plate is the primary factor that determines whether its resulting volcanic arc will produce tholeiitic basalt exclusively.

Cevap

Most volcanic arcs within the Cenozoic Belt are the result of tectonic plates subducting at an angle of 45 degrees or less.
By chaining the conditional statements, we establish that subducting at an angle greater than 45 degrees guarantees the volcanic arc will not produce tholeiitic basalt exclusively. The logical contrapositive dictates that if an arc DOES produce tholeiitic basalt exclusively, its subduction angle must be 45 degrees or less. Since the text explicitly states that most Cenozoic Belt arcs produce this basalt exclusively, it logically guarantees that most of them formed at subduction angles of 45 degrees or less.

Adım Adım Çözüm

1
Identify and diagram the first conditional premise.
Subduction angle > 45 degrees -> Arc distance > 200 km.
To establish the relationship between tectonic plate angle and arc distance.
2
Identify and diagram the second conditional premise.
Arc distance > 200 km -> NOT (Produces tholeiitic basalt exclusively).
To establish the relationship between arc distance and basalt composition.
3
Combine the first two premises into a transitive logical chain.
Subduction angle > 45 degrees -> NOT (Produces tholeiitic basalt exclusively).
To connect the initial condition (angle) to the final outcome (basalt composition).
4
Form the contrapositive of the transitive chain.
Produces tholeiitic basalt exclusively -> NOT (Subduction angle > 45 degrees), which means Subduction angle is 45 degrees or less.
To determine what must be true when the necessary condition is reversed and negated.
5
Apply the quantifier premise to the contrapositive rule.
Since MOST Cenozoic Belt arcs produce tholeiitic basalt exclusively, MOST Cenozoic Belt arcs must have subduction angles of 45 degrees or less.
To synthesize the formal logic chain with the factual quantifier provided in the stimulus, yielding the final provable deduction.

Anahtar Kavram

Chaining Conditional Statements and Quantifier Application
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Must Be True Questions

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