Hello!
I believe the correct answer would be: Both believe that a person sleeps for survival.
This is because the Adaptive sleep theory confirms that, for sure, sleep is essential. Core-Optional theory, on the other hand, has two parts to it: Optional and core sleep. One part is essential, and the other part isn't. So, you can say that both theories agree on the fact that you need to sleep for survival.
I hope my answer benefited you in some way! :)
*Plaigarism free.