Two statements are given below followed by two conclusions numbered $(1)$ and $(2)$. Which of the given conclusions logically follows from the two given statements? Please disregard commonly known facts.

Statements:
Some professors are doctors.
All the doctors are patients.

Conclusions:

1. Some professors are patients.
2. No doctor is professor.

Given,

Some professors are doctors.

All doctors are patients.

Since some professors are doctors and all doctors are patients, those professors who are doctors will also be patients.

So,

Some professors are patients.

Therefore, conclusion $(1)$ follows.

Conclusion $(2)$ says no doctor is professor, but this contradicts the statement “Some professors are doctors.”

So, conclusion $(2)$ does not follow.