Statements: All cars are cats. All fans are cats. Conclusions: All cars are…

Concept: When two universal statements share a common predicate — “All X are Z” and “All Y are Z” — X and Y are each independently linked to Z, but nothing in the statements fixes any relationship between X and Y themselves. A conclusion connecting X and Y can be treated as following only if it is forced to be true in every arrangement of X and Y that is consistent with both statements; if even one such arrangement makes it false, the conclusion does not follow.

Application: Here, Cars are a subset of Cats and Fans are a subset of Cats — both statements are universal and share the same predicate, Cats. Testing the two conclusions means checking every arrangement of Cars and Fans consistent with both statements: they could be two completely separate groups inside Cats, they could overlap partially, or one could sit entirely inside the other. In the fully separate arrangement, no car is a fan and no fan is a car, so both proposed conclusions fail together — and since that arrangement is fully consistent with the given statements, neither conclusion is forced to be true in every case.

Comparing the other options:

• Only conclusion (1) follows — this treats “all cars are fans” as certain, but the fully separate arrangement above is equally consistent with the statements and defeats it.

• Only conclusion (2) follows — this treats “some fans are cars” as certain, but the same fully separate arrangement defeats it too, since it requires no overlap at all between cars and fans.

• Either (1) or (2) follows — this either-or reading only applies when the two conclusions are a complementary pair that together must cover every possibility; the fully separate arrangement makes both false at once, so they are not such a pair.

Cross-check: Because the fully separate arrangement is never ruled out by the statements, and the two conclusions can fail simultaneously rather than forming a complementary either-or pair, no relationship between cars and fans can be pinned down from what is given.

Result: Neither conclusion (1) nor conclusion (2) follows from the statements.