I'm having some trouble working through the translation of the statement "A jolly clown is a tyrant. The book says "this is ambiguous, and to give two rival translations." I don't quite understand why though.
(Using: Jx : x is jolly, Cx : x is a clown, Tx : x is a tyrant).
My first intuition was to go with something like:
$ (\exists x)[(Jx \wedge Cx)\wedge (Tx)] $
(There exists a jolly clown that is a tyrant).
However the portion that says it ambiguous makes me think there is something I'm missing, and that it might be more akin to a conditional... like:
$ (\forall x)[(Cx \wedge Jx) \rightarrow (Tx)] $
(If a clown is jolly then they are a tyant).
Can anyone help me out by letting me know if I'm on the right track? Or provide some advice to my method?