Given that all assistants are agents and some agents are managers, can we conclude that some assistants are managers?

• A. No, not necessarily; the conclusion does not follow from the premises.
• B. Yes, some assistants must be managers.
• C. Yes, all assistants are managers.
• D. It depends on additional information.

Answer: (A)

The concept here is how subset relations and existence statements interact in logic. If all assistants are agents, then assistants form a subset of agents. If some agents are managers, that only tells us there exists at least one person who is both an agent and a manager. That person might or might not be an assistant, since being an agent does not guarantee being in the subset of assistants. So there could be managers who are not assistants, and no one who is both. A concrete way to see it is to imagine one person who is an assistant (and an agent) but not a manager, and another person who is a manager (and an agent) but not an assistant. This satisfies the given premises but shows that there need not be any overlap between assistants and managers. To conclude that some assistants are managers, we’d need additional information such as all agents being managers or all assistants being managers, or explicitly that some manager is an assistant.