Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:

All pigeons are ants.

Some ants are birds.

All birds are cats.

Conclusions:

I. Some cats are pigeons.

II. Some birds are pigeons.

III. Some cats are ants.

Let's analyze the statements logically:
Statement 1: All pigeons are ants. (Pigeons ⊆ Ants)

Statement 2: Some ants are birds. (Intersection exists between Ants and Birds)

Statement 3: All birds are cats. (Birds ⊆ Cats)

Now let's evaluate each conclusion:

Conclusion I: Some cats are pigeons.
There is no direct or necessary connection specified between cats and pigeons. Thus, this does not follow.

Conclusion II: Some birds are pigeons.
Pigeons are inside ants, and some ants are birds. However, it's not compulsory for the bird circle to intersect with the pigeon circle. Thus, this does not follow.

Conclusion III: Some cats are ants.
Since "Some ants are birds" and "All birds are cats", the portion of birds that are ants must also be cats. Therefore, there is definitely an intersection between cats and ants. This conclusion follows.

Hence, only conclusion III follows.