Question

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.

• A. Neither conclusion I nor II follows
• B. Only conclusion I follows
• C. Only conclusion II follows
• D. Both conclusions I and II follow

Hint:

When evaluating conclusions, if a connection is not explicitly stated or logically necessitated by the premises, consider it "not followed."

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem requires applying syllogistic logic to determine if the given conclusions are logically necessary consequences of the provided categorical statements.

Key Formula or Approach:
We represent the relations using set theory:
1. \( Z \subset Y \)
2. \( Y \cap X = \emptyset \)
3. \( X \subset W \)

Step 2: Detailed Explanation:
1. From statements (a) and (b), since all Zs are Ys and no Y is an X, it follows that no Z can be an X. This validates Conclusion II.
2. Conclusion I states "Some Ws are Zs". The statements provide information about the relationship of X to W, and Y to Z, but they do not provide any link between W and Z. In the absence of a direct or indirect link, we cannot conclude that any W is a Z.

Step 3: Final Answer:
Only conclusion II follows.