Statement:\nProstitution is also one of the main reasons for AIDS.\n\nConclusions:\nI. AIDS is an incurable disease.\nII. AIDS cannot be completely controlled by banning prostitution only.

Introduction / Context:
The statement attributes AIDS transmission partly to prostitution by saying it is also one of the main reasons. We must determine which conclusions necessarily follow, avoiding medical information not provided in the premise.

Given Data / Assumptions:

• AIDS has multiple main reasons; prostitution is among them.
• No information is provided about curability.
• The wording also implies there are other significant reasons beyond prostitution.

Concept / Approach:
Conclusion I (incurability) is outside the scope of the premise; curability relates to treatment outcomes, not causes. Conclusion II follows because if prostitution is only one among multiple main reasons, then eliminating prostitution alone cannot completely control AIDS; other transmission pathways would remain.

Step-by-Step Solution:
1) Parse also one of the main reasons → plurality of significant causes.2) Complete control by banning only one cause is logically insufficient → II follows.3) Curability (I) is a distinct dimension not addressed → I does not follow.

Verification / Alternative check:
Even if prostitution were eliminated, control would still require addressing other major vectors (not specified here), hence complete control cannot be guaranteed by a single-action ban.

Why Other Options Are Wrong:
Only I or Either/Both: import medical facts not present. Neither: ignores the logical effect of the phrase also one of the main reasons.

Common Pitfalls:
Confusing cause multiplicity with treatment efficacy; mixing domains of causation and cure.

Final Answer:
If only Conclusion II follows.