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Statements: Whenever the alarm rings, the gate closes automatically. The gate is now closed. Which conclusion is logically valid?

Competition practiceLogical / Critical
  • AThe alarm must have rung
  • BThe alarm certainly did not ring
  • CThe alarm rings only when the gate is already closed
  • DThe alarm may or may not have rung; a closed gate does not establish that it rang

Step-by-Step Solution

The rule says ringing leads to closing; it does not say that closing happens only through ringing. The gate could have been closed manually or by some other mechanism, so inferring the alarm from the closed gate would be affirming the consequent. The second option is equally unsupported and the third reverses the rule.
Answer: D) The alarm may or may not have rung; a closed gate does not establish that it rang

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