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A caretaker argues: 'If the overhead tank is refilled by noon, the afternoon supply runs without a break. The tank was not refilled by noon today. So the afternoon supply was broken today.' Which of the following sets out the form of this reasoning?

Competition practiceLogical / Critical
  • AIf P then Q; Q; therefore P
  • BIf P then Q; not P; therefore not Q
  • CIf P then Q; not Q; therefore not P
  • DIf P then Q; P; therefore Q

Step-by-Step Solution

The rule gives one way of securing an unbroken supply; it does not say that this is the only way. Water already standing in the tank, or a refill at one o'clock, would serve as well, so denying the stated condition settles nothing about the outcome. That is the form set out in the correct option. The third and fourth options are valid forms, and the first is a different error altogether.
Answer: B) If P then Q; not P; therefore not Q

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