I can use the following literals: Has(Batman,x), Slow(x), Fast(x), Car(x)
Batman has a fast car: Ex Car(x) ^ Fast(x) ^ Has(Batman,x)
All of Batman's cars are fast: Ax Car(x) ^ Has(Batman,x) -> Fast(x)
I'm pretty sure about these first two, kinda just want to make sure I'm doing them right. These I'm unsure about:
Unless Batman has a car, he is slow: Ax Car(x) ^ !Has(Batman,x) -> Slow(Batman)
The Batmobile is a fast car: Ex Car(x) ^ Has(Batman,x) ^ Fast(x)
Sorry I couldn't figure out how to make the formatting nice. Thanks for any help!
The first two sentences, with proper parenthesization, do the job.
The third item is not right. There are as usual many equivalent options. Something like this would work: $$\lnot \exists x(\text{Car}(x) \land \text{Has}(\text{Batman},x)) \longrightarrow \text{Slow}(\text{Batman}).$$ Equivalently, we could use $$\forall x(\lnot\text{Car}(x) \lor \lnot\text{Has}(\text{Batman},x)) \longrightarrow \text{Slow}(\text{Batman}).$$ Somewhat simpler is the equivalent $$\exists x(\text{Car}(x) \land \text{Has}(\text{Batman},x)) \lor \text{Slow}(\text{Batman}).$$
The problem with your version is that it says, among other things, that unless Batman has my car, he is slow.
For the last, if there were a constant symbol Batmobile, one could do it. As it is, one really cannot, we cannot assume that Batman has a car called the Batmobile. And even if we take it for granted that he does, the fact that rich boy Batman has a fast car doesn't imply the Batmobile is fast.