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If a soil sample contains high levels of manganese, then it is highly acidic. Furthermore, any soil that is highly acidic severely inhibits the growth of leguminous crops. However, agricultural surveys confirm that most soil samples from the Veridian region do not severely inhibit the growth of leguminous crops.

Which one of the following logically follows from the statements above?

  1. Most soil samples from the Veridian region do not contain high levels of manganese.Answer
  2. B
    If a soil sample from the Veridian region severely inhibits the growth of leguminous crops, it must contain high levels of manganese.
  3. C
    If a soil sample lacks high levels of manganese, it will not severely inhibit the growth of leguminous crops.
  4. D
    None of the soil samples from the Veridian region contain high levels of manganese.
  5. E
    Leguminous crops thrive more robustly in the Veridian region than in other regions with highly acidic soil.

Answer

Most soil samples from the Veridian region do not contain high levels of manganese.
The correct answer combines a transitive conditional chain with a contrapositive. The premises establish that High Manganese -> Highly Acidic, and Highly Acidic -> Inhibits Legumes. Linked together, High Manganese -> Inhibits Legumes. The contrapositive is that if soil Does NOT Inhibit Legumes -> NOT High Manganese. Because the stimulus states that MOST Veridian soil samples do not inhibit legumes, it logically follows that MOST Veridian soil samples do not contain high levels of manganese.

Step-by-Step Solution

1
Diagram the first conditional premise.
High Manganese -> Highly Acidic
This establishes the sufficient condition (manganese) and necessary condition (acidity).
2
Diagram the second conditional premise and chain it with the first.
Highly Acidic -> Severely Inhibits Legumes. Therefore, High Manganese -> Severely Inhibits Legumes.
Transitive logic allows us to connect the first condition directly to the final necessary condition.
3
Form the contrapositive of the chained statement.
Does NOT Severely Inhibit Legumes -> NOT High Manganese.
In conditional logic, negating the necessary condition allows us to negate the sufficient condition.
4
Apply the quantifier from the final premise to the contrapositive.
Since 'most' Veridian samples do NOT severely inhibit legumes, 'most' Veridian samples must NOT have High Manganese.
Applying a 'most' statement to the sufficient condition of a valid conditional rule allows us to conclude 'most' for the necessary condition.

Key Concept

Chaining conditional statements, forming contrapositives, and combining them with quantity indicators (most).
Estimated Time:1m 30s
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