Three 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:
Some wallets are purses.
Some purses are bags.
All bags are suitcases.

Conclusions:
I. No wallet is a suitcase.
II. Some purses are suitcases.
III. All wallets being bags is a possibility.

Let's analyze the statements using Venn diagrams:
"Some wallets are purses" → Intersection between Wallets and Purses.

"Some purses are bags" → Intersection between Purses and Bags.

"All bags are suitcases" → The entire circle of Bags is inside Suitcases.

Now let's evaluate the conclusions:

Conclusion I: "No wallet is a suitcase." Since there is no negative statement limiting Wallets and Suitcases, they can overlap. Thus, "No wallet is a suitcase" is not definitely true in all cases. So, Conclusion I does not follow.

Conclusion II: "Some purses are suitcases." Since "Some purses are bags" and "All bags are suitcases", the part of purses that is bags must also be suitcases. Therefore, this conclusion is definitely true and follows.

Conclusion III: "All wallets being bags is a possibility." There is no restriction preventing all wallets from being inside the bags circle. Thus, it is a valid possibility. Conclusion III follows.

Hence, only conclusions II and III follow.