Which of the following statements are logically equivalent?

A. All aeroplanes are polluting vehicles.

B. No polluting vehicles are aeroplanes.

C. All non-polluting vehicles are non-aeroplanes.

D. No aeroplanes are non-polluting vehicles.

Choose the correct answer from the options given below:

The correct answer is A, C and D only
Important PointsIn logic, a statement and its contrapositive are considered logically equivalent. The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then swapping the order.

A. "All aeroplanes are polluting vehicles." This is a general statement of the form: If it's an aeroplane, then it's a polluting vehicle.

C. "All non-polluting vehicles are non-aeroplanes." This is the contrapositive of Statement A.

• It negates both parts of the original statement and reverses their order. So, if it's not a polluting vehicle, then it's not an aeroplane.
• Both A and C convey the same information, but from different perspectives. Hence, they are logically equivalent.

D. "No aeroplanes are non-polluting vehicles." This statement is saying the same thing as Statement A, but in a different format.

• It's stating that there are no aeroplanes that aren't also polluting vehicles, which is just another way of saying all aeroplanes are polluting vehicles. Hence, it's logically equivalent to Statement A and Statement C.