Here's the question:

Let P(x) denote the statement "x is a professional athlete," and let Q(x) denote the statement "x plays soccer." The domain of discourse is the set of all people. Write each proposition in words. Determine the truth value of the statement.

(upsidedown A)x (P(x) --> Q(x))

Sorry I do not know how to do symbol of upside down A but i'm sure you guys know what I mean.. so here is it in words:

All profesional athletes play soccer.

How do I determine whether a statement is true or false? Obviously this one is false just by reading it, but is there a certain way to prove it is false?

To add in another statement..

(backwards E)x (Q(x) --> P(x))

I thought this meant:

"For some people, they are a professional athlete if they play soccer."

Is this right? How do I prove if the statement is true or false value?