For a given predicate $P(x),$ you might believe that the statements AAxP$(x)$

or EExP$(x)$ are either true or false.

How would you decide if you were correct in each case? You have four choices:

you could give an example of an element $n$ in the domain for which $P(n)$ is

true or for which $P(n)$ if false,

or you could argue that no matter what $n$ is$,P(n)$ is true or is false.

$($a$)$ What would you need to do to prove AAxP$(x)$ is true?

$($b$)$ What would you need to do to prove AAxP$(x)$ is false?

$($c$)$ What would you need to do to prove EExP$(x)$ is true?

$($c$)$ What would you need to do to prove EExP$(x)$ is false?