If-then statement problems 
*

*Your guarantee is good only if you bought your CD player less than 90 days ago.

*If your guarantee is good, then you must have bought your CD player less than 90 days ago.

Can we also write the if-then statement of the sentence of this link like the following:

if  you have bought a CD player less than 90 days ago then the guarantee
is good

If I am wrong then please correct me.
Edit: Thanks for the answers
 A: You are not correct. "If $P$, then $Q$" is equivalent to "$P$ only if $Q$" ($P \rightarrow Q$ In symbolic notation). In this case, $P \equiv$ "Your guarantee is good" and $Q \equiv$ "You bought your CD player less than 90 days ago". So, the given statements are equivalent to $P \rightarrow Q$, but the one you stated is equivalent to $Q \rightarrow P$.
A: The statement that you presented is not equivalent to the one presented in the picture.
Note the following. Let $p$ and $q$ be any statements. The statement $p \implies q$ means “if $p$ then $q$”, or equivalently, “$p$ only if $q$.” (Note that this is what is written in the picture).
Your statement is $q \implies p.$ And you can easily see that they are not equivalent.
If $v(p) = T$ and $v(q) = F,$ then $v(p \implies q) = F$ but $v(q \implies p) = T.$ So $p \implies q$ and $q \implies p$ are not equivalent statements.
In short, you have the following.
$$\begin{align}
p \implies q & \quad \text{If $p,$ then $q$}\\
& \quad\text{$p$ only if $q$}\\
\quad \\
q \implies p & \quad \text{If $q,$ then $p$}\\
& \quad \text{$q$ only if $p$}
\end{align}$$
A: These kinds of unclear situations can largely be avoided by phrasing the sentences with “it follows” instead of “if”.


*From the fact that your guarantee is good, it follows that you must have bought the CD player <90 days ago.

(Note that the first version can not directly be phrased in this version.)
So that mean indeed the correct direction is guarantee → time-since-buy.
$$
  \text{valid}(\text{guarantee}) \Longrightarrow t_\mathrm{buy} <90\:\mathrm{d}
$$
The other direction is not true, as witnessed by the real-world situation that the warrantee is also void if you smash the CD player on the floor – then $t_\mathrm{buy} <90\:\mathrm{d}$ would still be fulfilled, but you could not conclude that the guarantee is still valid.
What does work is, turning around the implication arrow whilst also negating the statements.

From the fact that you have not bought the player <90d ago, it follows that the guarantee is void.

$$
  \neg(t_\mathrm{buy} <90\:\mathrm{d}) \Longrightarrow 
 \neg(\text{valid}(\text{guarantee}))
$$
