I would like to represent the statement
"There is a student registered to AI class who talks to other students that are registered to AI class."
to first order logic. I have come up with this but I am not sure if it is the correct solution:
$\exists x,y: \text{Student}(x) \wedge \text{Student}(y) \wedge \text{TakesAI}(x) \wedge \text{TakesAI}(y) \wedge \text{Talk}(x,y)$
I think it means there are two students that take AI and they talk. Should I change my answer to this:
$\exists x,y: \text{Student}(x) \wedge \text{Student}(y) \wedge \text{TakesAI}(x) \wedge \text{TakesAI}(y) \Rightarrow \text{Talk}(x,y)$
I changed the last "and" operator to make it sound like: "If there are two students that take AI, they are talking."
Which do you think is better? What seems like to be the difference? How would you represent the statement in FOL?
Thank you for your answers.
Best Answer
The first one is correct.
The second one says that there are two people such that if they are both students and take AI, then they talk. This is automatically satisfied by any two people (well, depending on what you're quantifying over, perhaps they don't even need to be people) who are not both students who take AI, whether or not they talk, so it says practically nothing.