Let W, X, Y, Z be some entities.
Statements: a) All Zs are Ys. b) No Y is a X. c) Every X is a W. Conclusions: I. Some Ws are Zs. II. Zs are not Xs.Step-by-step Solution:
From statement (a) we know \( Z \subset Y \). From statement (b) we know the intersection of Y and X is empty (\( Y \cap X = \emptyset \)). Since all Zs are within Y, and Y completely excludes X, Z must also completely exclude X. This makes Conclusion II ("Zs are not Xs") TRUE. From statement (c) we know \( X \subset W \). While W contains X, there is no relationship defined that forces W to overlap with Z. W could exist entirely separately from Z. Therefore, Conclusion I ("Some Ws are Zs") is not necessarily true. Hence, only conclusion II follows.