Correct Option
The problem statement specifies, "Only one of A and B is open during storms." This condition directly establishes that in the event of a storm, either road A or road B will be operational. Consequently, it is guaranteed that at least one road remains open during storms. Therefore, the statement "During storms at least one road is open" is correct.
Incorrect Options
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Under normal conditions only three roads are open:
This statement is not necessarily true. Under normal conditions, one road from the set {A, P, R} is open. Road C has no specified closure conditions, implying it is generally open. The status of roads B and Q can vary. For instance, if road A is open, C is open, B is open, and Q is also open (as Q can be open if B is open), then four roads (A, C, B, Q) would be operational. Thus, the number of open roads is not restricted to exactly three.
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During floods only three roads are open:
This statement is also not necessarily true. During floods, road P is closed. Given that "Only one out of A, P and R is open at any one time," it implies that either road A or road R must be open. Road C remains open as no flood-specific closure is mentioned for it. If, additionally, road B is open, then road Q can also be open (since "If B is closed, so is Q" means Q can be open if B is open). In such a scenario, roads (A or R), C, B, and Q could all be open, totaling four roads. Therefore, the number of open roads is not limited to three.
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During calamities all roads are closed:
This statement is incorrect. As determined in the analysis for Option B, during storms, at least one road (A or B) is open. Furthermore, during floods, at least one road (A or R) is open, and road C is also open. Therefore, it is not possible for all roads to be closed during calamities like storms or floods.