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Difficulty: Very hardDrawing Valid Inferences

Paleoclimatological analysis of ice core samples from the Devon Ice Cap revealed distinct volcanic ash layers corresponding to historical eruptions. Samples containing volcanic glass with a silica content exceeding 70%70\% were formed exclusively during explosive eruptions of stratovolcanoes, whereas glass with lower silica content originated from shield volcanoes. Furthermore, high-sulfate deposits were observed only in ice layers where the atmospheric temperature at the time of deposition was recorded below −15∘C-15^\circ\text{C}. The analysis established that every ice layer containing volcanic glass from a stratovolcano also contained high-sulfate deposits, yet fewer than half of the layers with high-sulfate deposits contained any volcanic glass whatsoever.

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

  1. A
    Explosive eruptions of stratovolcanoes consistently cause localized atmospheric temperatures to drop below −15∘C-15^\circ\text{C}.
  2. Any ice core layer in the sample containing volcanic glass with a silica content exceeding 70%70\% was deposited under atmospheric temperatures below −15∘C-15^\circ\text{C}.Answer
  3. C
    Any ice layer deposited when the atmospheric temperature was below −15∘C-15^\circ\text{C} will display high-sulfate deposits.
  4. D
    Eruptions from shield volcanoes never result in high-sulfate deposits in ice core layers.
  5. E
    More than half of the ice core layers with high-sulfate deposits contained volcanic glass originating from shield volcanoes.

Answer

Any ice core layer in the sample containing volcanic glass with a silica content exceeding 70%70\% was deposited under atmospheric temperatures below −15∘C-15^\circ\text{C}.
The correct option synthesizes three explicit facts from the passage into a valid conditional chain. Silica content exceeding 70%70\% identifies the glass as originating from a stratovolcano. The passage explicitly states that every layer containing stratovolcano glass has high-sulfate deposits. Finally, high-sulfate deposits occur exclusively in layers deposited when atmospheric temperatures were below −15∘C-15^\circ\text{C}. Following this chain of necessary conditions proves that any layer containing glass with >70%>70\% silica must have been deposited under temperatures below −15∘C-15^\circ\text{C}.

Step-by-Step Solution

1
Extract premise 1 regarding silica content.
Volcanic glass with silica >70%  ⟹  > 70\% \implies stratovolcano origin.
Establishes the definition of stratovolcano glass layers.
2
Extract premise 2 regarding stratovolcano layers and sulfate deposits.
Stratovolcano glass layer   ⟹  \implies high-sulfate deposit present.
Connects stratovolcano glass presence to high-sulfate presence.
3
Extract premise 3 regarding sulfate deposits and temperature constraints.
High-sulfate deposit present   ⟹  \implies atmospheric temperature <−15∘C< -15^\circ\text{C}.
The phrase 'observed only in ice layers where temperature was below −15∘C-15^\circ\text{C}' establishes temperature as a necessary condition for high-sulfate deposits.
4
Chain the conditional statements logically.
Silica >70%  ⟹  > 70\% \implies stratovolcano origin   ⟹  \implies high-sulfate deposit   ⟹  \implies temperature <−15∘C< -15^\circ\text{C}.
Transitive property of conditional logic dictates that any layer with silica >70%> 70\% must have been deposited at temperatures below −15∘C-15^\circ\text{C}.

Key Concept

Conditional Logic Chaining and Transitive Inferences
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Topics

Drawing Valid Inferences

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