Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements: All A are B.
Some A are C.

Conclusions: I. Some B are C.
II. No C is B.
III. Some B are A.

Let's test the validity of each conclusion using logical relations:
Statements:

All A are B.

Some A are C.

Conclusions:

Conclusion I: Some B are C.

Since all A are inside B, and some parts of A intersect with C, that overlapping part of A is definitely inside B. Thus, some B are automatically C. This conclusion follows.

Conclusion II: No C is B.

Since Conclusion I is definitely true, Conclusion II is completely false and does not follow.

Conclusion III: Some B are A.

Since all A are B, the region occupied by A is part of B, meaning some B are definitely A. This conclusion follows.

Therefore, only conclusions I and III follow.