Trouble understanding only one way implication truth
Solution 1:
For real numbers:
$$x > 1$$
implies that $$ x^2 > 1 $$
But $x^2 > 1$ does not imply that $x > 1$. For instance, $(-2)^2 = 4 > 1$, but $-2$ is not greater than $1$.
Solution 2:
$x = 2 \implies x \ge 2$ is true.
$x \ge 2 \iff x = 2$ is false.