Prompt:
"I will give you a logic puzzle. You should first write [Reasoning] and explain your reasoning. Then write [Answer] and write your answer. Ready?"
I then gave it the original puzzle and got this.
Answer:
"[Reasoning]
We are given two statements:
If it rains today, I will drive home.
I did not drive home.
The first statement is a conditional statement, meaning that if the condition "it rains today" is true, then the outcome "I will drive home" will also be true. However, the second statement tells us that the outcome "I did not drive home" is true.
In logic, this is an example of Modus Tollens, which states that if we have a conditional statement (if P, then Q) and the negation of the consequent (not Q), we can infer the negation of the antecedent (not P). In this case, P represents "it rains today" and Q represents "I will drive home."
[Answer]
Since we know that the outcome "I did not drive home" is true (not Q), we can infer that "it did not rain today" (not P)."
GPT-4, seems solid. It also solves the original without any issue but gives a simpler answer:
"Based on the information provided, it can be inferred that if it rains today, you will drive home. However, you mentioned that you did not drive home. From this, we can conclude that it likely did not rain today."
I then gave it the original puzzle and got this.
Answer: "[Reasoning] We are given two statements:
If it rains today, I will drive home. I did not drive home. The first statement is a conditional statement, meaning that if the condition "it rains today" is true, then the outcome "I will drive home" will also be true. However, the second statement tells us that the outcome "I did not drive home" is true.
In logic, this is an example of Modus Tollens, which states that if we have a conditional statement (if P, then Q) and the negation of the consequent (not Q), we can infer the negation of the antecedent (not P). In this case, P represents "it rains today" and Q represents "I will drive home."
[Answer] Since we know that the outcome "I did not drive home" is true (not Q), we can infer that "it did not rain today" (not P)."
GPT-4, seems solid. It also solves the original without any issue but gives a simpler answer:
"Based on the information provided, it can be inferred that if it rains today, you will drive home. However, you mentioned that you did not drive home. From this, we can conclude that it likely did not rain today."