What is a valid inference from a NO/NONE statement?

• A. If in Group A, then NOT in Group B.
• B. All members of Group B have quality B.
• C. Some members of Group A have quality B.
• D. If in Group B, then Group A.

Answer: (A)

When a NO/NONE statement is given about two groups, it means those groups don’t overlap at all. In other words, nothing can be in both groups. From that, if something is in Group A, it cannot be in Group B. That makes the inference: If in Group A, then not in Group B.

Why the other ideas don’t follow: a statement about no overlap doesn’t say anything about all members of Group B having a certain quality, nor does it assert that some members of Group A have that quality. It also doesn’t imply that being in Group B would force membership in Group A. The NO/NONE relationship only guarantees that membership in one group excludes membership in the other.