Question

The question below consists of a main statement followed by four options. Select the one that logically follows the main statement
If I drive a car, then it is a BMW or a Skoda.

• A. I am driving a car, means that it is a BMW or a Skoda
• B. The car is neither BMW nor a Skoda, hence I do not drive a car.
• C. I drive a car but it is not a Skoda, means it is a BMW
• D. All the above

Answer 1

The Correct Option is D

To solve this logical reasoning question, we need to analyze the main statement and determine which options logically follow it.

Main Statement: If I drive a car, then it is a BMW or a Skoda. 

This statement is a conditional one and can be represented in logical terms as:

\(P \rightarrow (Q \lor R)\)

• \(P\): I drive a car
• \(Q\): The car is a BMW
• \(R\): The car is a Skoda

Let's evaluate the options based on this logical representation:

1. I am driving a car, means that it is a BMW or a Skoda: 
   This option is directly supported by the logical statement \(P \rightarrow (Q \lor R)\). Therefore, this option is true.
2. The car is neither BMW nor a Skoda, hence I do not drive a car: 
   This is the contrapositive of the main statement, which is logically equivalent. The logical contrapositive of \(P \rightarrow (Q \lor R)\) is \(\neg(Q \lor R) \rightarrow \neg P\). Since a contrapositive is always true if the original statement is true, this option is also correct.
3. I drive a car but it is not a Skoda, means it is a BMW: 
   This statement also follows logically from the main statement. If you drive a car and it is not a Skoda, then it must be a BMW to satisfy \(Q \lor R\) being true. Hence, this option is true as well.
4. All the above: 
   Since all the individual statements are correct based on our evaluation, this option is also correct.

Therefore, the correct answer is All the above.