If the domain consists of all integers, what are the truth values of these statements?
a) $\exists ! x \ (x>1)$
Because the domain consists of all integers then we can loop through all $n$ values of $x$. Besides this wee see that $P(x)$ can only be truth with a domain of positive integers except $1$. So $\exists ! x \ P(x)$ is false.
Am I right?
The statement says that there is a unique integer greater than $1$, i.e. there is only one integer greater than $1$. This is obviously false.