Final answer:
None of the options A) Quigley arrives, B) Rockville arrives, C) Wooster arrives, or D) York arrives must necessarily be true if Tilbury does not arrive, as the conditions provided are dependent on other trains' arrivals, not on Tilbury's absence.
Step-by-step explanation:
The question is a logic puzzle where the arrival of certain trains is contingent upon the arrival or absence of other trains. If Tilbury does not arrive, we cannot make direct inferences about the arrivals of Quigley, Rockville, or Wooster, since their arrivals are dependent on other trains' arrivals. However, there is no condition that states a requirement for York to arrive based only on Tilbury's absence, nor are there any conditions that negate York's arrival should Wooster not arrive.
Therefore, none of the options A) Quigley arrives, B) Rockville arrives, C) Wooster arrives, or D) York arrives must be true if Tilbury does not arrive. Each of the conditions given in the question depends on the presence of another train, not on the absence of Tilbury. Without specific conditions that determine the necessity of another train's arrival when Tilbury does not arrive, we cannot conclude that any of the given trains must necessarily be at Middlebrook station.