Three statements are given, followed by three conclusions I, II and III. You…

Concept: When two of the offered conclusions state "Some X are Y" and "No X is Y" about the exact same pair of terms, they are logical contradictories: for any real relationship between X and Y, exactly one of the two must be true, even when the premises never fix which one. This is the standard either-or case in syllogism, and it can hold even though neither conclusion is individually certain.

Application: Given premises:

• Some rats are cats.

• No cat is a crow (so no crow is a cat).

• All crows are parrots.

Checking each conclusion:

• Conclusion (I) Some parrots are cats. — The premises fix that crows, a subset of parrots, are never cats, but they say nothing about whether the remaining, non-crow parrots overlap cats, so this is not guaranteed on its own.

• Conclusion (II) No parrot is cat. — For the same reason, whether the non-crow parrots avoid cats entirely is also left open, so this alone is not guaranteed either.

• Conclusion (III) Some rats are crows. — Rats are linked only to cats, and cats are kept completely separate from crows; no premise connects rats to crows, so this fails outright and cannot combine with (I) or (II).

Either-or check: Conclusions (I) and (II) describe the only two possible parrot–cat relationships — some overlap, or none — together they cover every case, so one of them is always true even though which one depends on details the statements don't supply.

Cross-check: Two scenarios satisfy all three statements: (a) the only parrots are the crows, so parrots and cats never overlap — (II) holds, (I) fails; (b) parrots also include a non-crow member that is a cat — (I) holds, (II) fails. Both scenarios keep (III) false, since neither ever forces a rat to be a crow.

Only either Conclusion (I) or (II) follows.