Connectives in predicate logic

Question

How do I translate the following to predicate logic:

D(x) - x is a bus driver

P(x) - x is a passenger

There are no passengers but there is a bus driver.

For the passengers ¬∃x P(x) and ∃ D(x) for the driver, but how do I join the two with the connective "but".

Answer 1

The English word "but" is formally symbolized as a conjunction in predicate logic.

Therefore the correct symbolization is as follows:

$$\neg \exists x P(x) \wedge \exists x D(x)$$

This means there doesn't exist an x such that x is a passenger (there are no passengers) and there exists an x such that there is a bus driver (there is at least one bus driver).