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How to show "if and only if"?

For example:

Show that $x(t) \ge 0$ if and only if $x_e(t) \ge |x_o(t)|$ for all values of $t$, where $x_e(t)$ is the even part of $x(t)$ and $x_o(t)$ is the odd part of $x(t)$.

Is it enough to show that the first condition is true if the second condition is true? Do I also need to show that it is false if the second condition is false?

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    First condition: I am alive . Second condition: I feel sleepy. First is true if second is. Not the other way around.They are not logically equivalent. "X iff Y" can't be true unless X,Y must be both true or both false. – 2017-01-16

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If and only if is two implications and you have to justify both. If you just have two sentences $A$ and $B$, and prove $A \implies B$ it could be that $A$ is false and $B$ is true. Then it is not true that $B \implies A$. You can either prove $B \implies A$ or $\lnot A \implies \lnot B$, as they are equivalent.

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    What is the meaning of $\lnot$ symbol? – 2017-01-15
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    $\implies$ is implies, so $A \implies B$ is if $ A$ then $ B$. $\lnot$ is not. – 2017-01-15