The question asks about the truth of a conditional statement and its converse based on given premises. Let's break it down step by step.

Given Information:

1. The statement "Peter drives faster than the speed limit" is false.
2. The statement "Peter runs a red light" is false.
3. The statement "Peter will have to pay a fine" is false.

Now, the question is based on the conditional statement:

"If Peter drives faster than the speed limit or runs a red light, then he will have to pay a fine."

And it also asks about its converse:

The converse would be: "If Peter has to pay a fine, then he drove faster than the speed limit or ran a red light."

Step 1: Analyze the original conditional statement

The structure of the original statement is:
$\text{If } A \text{ or } B, \text{ then } C$

Where:

• $A$: Peter drives faster than the speed limit (false).
• $B$: Peter runs a red light (false).
• $C$: Peter will have to pay a fine (false).

If both $A$ and $B$ are false, and $C$ is also false, the implication ("If A or B, then C") would still hold true in classical logic, because an implication is only false if the hypothesis is true and the conclusion is false. Since the hypothesis ("Peter drives faster or runs a red light") is false, the conditional statement is considered true regardless of the conclusion.

Step 2: Analyze the converse

The converse is:
$\text{If } C, \text{ then } A \text{ or } B$

Where:

• $C$: Peter will have to pay a fine (false).

Since $C$ is false, the converse can also be considered true for the same reason: in classical logic, a false antecedent makes the entire implication true.

Conclusion:

Both the original statement and the converse are true. Thus, the correct answer is:

• The statement and the converse are both true.

Would you like more details or have any questions?

Here are 5 questions related to this topic:

1. What is the difference between a conditional statement and its converse?
2. How does classical logic handle false premises in conditional statements?
3. Can a conditional statement be true even if all parts are false?
4. What is the inverse of a conditional statement, and how is it evaluated?
5. How do different logical systems (like intuitionistic logic) treat implications?

Tip: In logic, a conditional statement is only false when the hypothesis is true, and the conclusion is false.