Existence, Uniqueness and Counterexamples · Challenge problem

$x^2 > 4$ if and only if $x > 2$ (for real $x$)

$n$ is prime if and only if $2^n - 1$ is prime

$n$ is even if and only if $n^2$ is divisible by $8$

$x^2 < 4$ if and only if $-2 < x < 2$ (for real $x$)