The notation
$\exists !x P(x)$
denotes the proposition
" There exists a unique x such that P(x) is true. "
If the universe of discourse is the set of integers, what are the truth values of the following?

 1. $\exists !x (x>1)$
 2. $\exists !x (x^2=1)$
 3. $\exists !x (x+3=2x)$
 4. $\exists !x (x=x+1)$