Hello, kmjt!

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.

"All professional athletes play soccer." . Correct!

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?

We are supposed to use our knowledge.

As you said, the statement is not true.

. . There are professional athletes who play baseball, tennis, etc.

I thought this meant:

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

This is correct, but awkward.

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

I would write "Some soccer players are professional athletes."

Since there are entireteamsof professional soccer players,

. . we know that this statement is true.