I'm having some trouble representing the following situation:
There are three persons of unique names: Lars, Kirk and James. Each person drinks a unique beverage: beer, vodka and whiskey. Each person drives unique cars (brand): Mercedes, BMW and Wolkswagen. It is known that:
- James drinks whiskey
- Kirk drives BMW
- The man driving BMW drinks beer
- The person who drives Mercedes also drinks vodka.
I think I can represent the situation as follows (correct me if I'm wrong):
- $Whiskey(James)$
- $BMW(Kirk)$
- $\forall(x) BMW(x) \rightarrow Beer(x)$
- $\forall(x) Mercedes(x) \rightarrow Vodka(x)$
It is stated that only one person can drive BMW (like the other cars as well). Do I have to specify uniqueness for all of the variables, that is for drinks and car brands like the following?
- $\exists x (BMW(x) \wedge \neg \exists y (BMW(y) \wedge x \ne y)) $
Or is there a shorter approach to state the uniqueness of all these things?