Three statements are given followed by three conclusions I, II and III. Assuming that the information given in the statements is true, even if it seems to be at variance with commonly known facts, decide which of the given conclusions logically follows from the statements.
Statement :
No mug is bucket.
All mugs are cups.
Some cups are spoons.

Conclusion:
I. Some spoons are buckets.
II. Some mugs are spoons.
III. Some cups are not buckets.

Let's evaluate the relations using set theory / Venn diagrams:
Mug∩Bucket=∅ (No mug is a bucket)

Mug⊆Cups (All mugs are cups)

Cups∩Spoons

=∅ (Some cups are spoons)

Now let's check each conclusion:

Conclusion I: "Some spoons are buckets." There is no definitive connection given between spoons and buckets. It may or may not be true. Hence, it does not logically follow.

Conclusion II: "Some mugs are spoons." Spoons intersect with cups, but not necessarily with mugs. Hence, it does not logically follow.

Conclusion III: "Some cups are not buckets." Since all mugs are cups, that specific part of cups which are mugs cannot be buckets (because no mug is a bucket). Thus, the cups that are mugs are definitely not buckets. This conclusion always follows.

Therefore, only conclusion III follows.