Let $L'$ be a context-free language. If $L \leq_M L' \leq_M L''$, where $\leq_M$ denotes mapping reducibility (aka many-one reducibility), what can we know about $L$ and $L''$?
I think they're both decidable languages but that's all I can say.
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From $L \leq_M L' \leq_M L''$, we can only conclude that $L$ is decidable. It is because $L'$ is a context free language and hence decidable (If you need a proof, you can take a look at this Are all context-free and regular languages efficiently decidable?) . So, we can convert $L$ to $L'$ and then decide $L$.
But we can not do the same for $L''$. Because it might be possible to reduce $L'$ to $L''$ but after reduction we can not say that it can be decided in that reduced form.
