Question

T an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor, the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition:

If the cars on the first floor are sports cars, then the cars on the second floor are new. If the cars on the third floor are research models, then the cars on the first floor are family cars.
If the cars on the second floor are used, which of the following must be true?
A)The cars on the first floor are family cars
B)The cars on the third floor are research models
C)The cars on the first floor are sports cars
D)The cars on the third floor are production models

Answer 1

When the cars on the second floor are used, none of the provided options (A, B, C, D) must be true since the given conditions in the question do not allow us to conclude the status of cars on the first or third floors.

Step-by-step explanation:

To determine which statement must be true if the cars on the second floor are used, we will examine the given conditions about the automobile exhibition:

• If the cars on the first floor are sports cars, then the cars on the second floor are new.
• If the cars on the third floor are research models, then the cars on the first floor are family cars.

Since the cars on the second floor are used, the conditional statement concerning the first floor being sports cars and the second floor being new is not applicable. Therefore, we can say nothing about the first floor's cars based on the second floor's condition. However, for the third floor, the absence of information regarding if they are research models means we cannot determine their type based on the provided information.

Therefore, none of the options A, B, C, or D can be determined as necessarily true with certainty based on the condition that the cars on the second floor are used. Thus, the answer is that none of the provided statements must be true.