MHB Can Predicate Properties Be Neither True nor False?

[lemonthree]

I'm not very sure whether a predicate can be neither true or false, and I haven't seen any example so far.

The second choice is false because it is the truth set that is the set of all values which make the predicate true.
A predicate has finite variables, so the third choice is false too.

I believe the truth set of a predicate can be empty, so the last choice is true.

 

[Evgeny.Makarov]

I agree with your choices, but I find the questions not precise enough. According to Wikipedia, a predicate on a set $X$ is a function from $X$ to $\{\text{true}, \text{false}\}$. With this definition it is not clear what "always" means in question 1 and what it means for a predicate to contain variables in question 3.