In the following question, the main statement is followed by four sentences. Select a pair of sentences that relate logically to the given statement.
Statement : Either the train is late, or it has derailed.
a. The train is late.
b. The train is not late.
c. The train is derailed.
d. The train is not derailed.

Correct option is A

Given Statement:

"Either the train is late, or it has derailed."

This is a logical "either/or" statement, meaning one of these two conditions must be true, and not both.

Logic Breakdown:

The two possible scenarios are:

1. The train is late.
2. The train has derailed.

So, the statement indicates that either the train is late or it has derailed. If one condition is false, the other must be true.

Analyzing Each Sentence:

• a. The train is late.

  • If this is true, then the first part of the "either/or" statement is satisfied. We do not need to consider the second condition (train derailed) since the first condition is true.

• b. The train is not late.

  • If the train is not late, then for the "either/or" statement to hold, the train must have derailed. This would make the second part of the statement true.

• c. The train is derailed.

  • If this is true, then the second part of the "either/or" statement is satisfied. The train does not need to be late, as the second condition is satisfied.

• d. The train is not derailed.

  • If the train is not derailed, then for the "either/or" statement to hold, the train must be late. This would make the first part of the statement true.

Now, let's evaluate the answer choices:

• Option A (bc):

  • If the train is not late (b), then it must be derailed (c). This follows logically, so this pair works.

• Option B (ca):

  • This implies the train is derailed (c) and also late (a), which contradicts the "either/or" structure since both conditions can't be true at the same time. Therefore, this pair is not logically correct.

• Option C (ab):

  • If the train is late (a), then it does not necessarily need to be derailed. This satisfies the "either/or" statement, so this pair works as well.

• Option D (db):

  • If the train is not derailed (d), then it must be late (b) to satisfy the "either/or" statement, which is logically consistent. This pair also works.

Conclusion:

The pairs (a) and (b), (c) and (a), and (d) and (b) are all logically correct. However, since we need to choose the most appropriate answer, Option A (bc) is the best fit because it clearly satisfies the "either/or" condition.