What is the logic symbol to write: $D$ only when $P$ The text I am reading gives this problem:
Express the following using logic symbols.
The cat is out of the bag only when the contestant is bald.  
$D$ is:  The cat is out of the bag, and $P$ is: The contestant is bald, thus $D$ only when $P$.
I thought of "only when" as similar to "only if" and  answered $D \iff P$.  The text gives the answer as $D \implies P$.
That then is:
If the cat is out of the bag, then the contestant is bald, and I can not see that "if-then" has the same meaning as "only when".  
As an absolute amateur at this, and assuming that the text is not in error, I have to look here for guidance.  The logic text I am reading makes it very clear that connections do not imply causality or sequence in time.  "Only when" does not imply a sequence, but does seem to separate the times when the contestant is bald and when, another, contestant is not.  Please excuse me if I am not making sense about this.
How do I interpret "only when"?
 A: We read $D\implies P$ as "if $D$ then $P$," but what the notation really means is
"either $D$ is false or $P$ is true or both."
Given that $D \implies P,$ is it possible that $D$ is true when $P$ is false?
No, because then neither of the two halves of the "either or" version of the statement is true: it is not true that $D$ is false and it is not true that $P$ is true.
So the statement $D\implies P$ tells us that the only circumstances under which $D$ can be true are when $P$ also is true. "$D$ true and $P$ false" is ruled out.
Hence $D$ is true only when $P$ is true.

Another way to think of this is to recall that we read
$D \iff P$ as "$D$ if and only if $P.$"
Now, "$D$ if $P$" is the same as "if $P$ then $D$", that is, it can be written
$P \implies D$ or $D \impliedby P$.
So the "if" half of the "if and only if" gives us the $D \impliedby P$ direction of the arrow in $D \iff P$.
The other direction of the arrow, $D \implies P$, is given by the "only if".
That is, "$D$ only if $P$" is a legitimate way to read $D\implies P$.
A: "$D$ only when $P$" means exactly that "not $D$ when not $P$".   That is $\neg P\to\neg D$.

If it is $D$ only when it is $P$, then it must be not $D$ when it is not $P$.
If it is not $D$ when it is not $P$, then it can be $D$ only when it is $P$.

"$D$ only when $P$" also means exactly that "$P$ when $D$".  
That is $D\to P$.

If it is $D$ only when it is $P$, then it must be $P$ when it is $D$.
If it is $P$ when it is $D$, then it must be $D$ only when it is $P$.

