Syllogism — “All beggars are poor.” Which conclusion is most reasonably drawn if “poor” and “rich” are mutually exclusive economic states in this context?

Introduction / Context:
This item examines basic categorical logic. The premise is “All beggars are poor.” In many exam settings, “poor” and “rich” are treated as disjoint categories (mutually exclusive). Within that conventional interpretation, we must select the most justified conclusion.

Given Data / Assumptions:

• Premise: beggar ⇒ poor.
• Contextual assumption: poor and rich are mutually exclusive labels.
• Goal: choose the conclusion that safely follows.

Concept / Approach:
From beggar ⇒ poor and poor ∧ rich are incompatible, it follows that beggar ⇒ not rich. We avoid converses or overgeneralizations not supported by the premise.

Step-by-Step Solution:

Verification / Alternative check:
Examine other candidates: the converse “if not rich then not a beggar” (option b) is invalid; many not-rich people are not beggars. “All poor are beggars” (option c) overgeneralizes. “If rich then not a beggar” (option d) could be true under exclusivity, but it does not directly follow from “all beggars are poor” alone without the added premise about poor vs rich; option (a) captures the direct chain reasoning more transparently from the given plus the standard assumption.

Why Other Options Are Wrong:

• (b) Converse error.
• (c) Illicit conversion of universal affirmative.
• (d) States a contrapositive of the added exclusivity premise rather than the primary chain from “beggar ⇒ poor.”

Common Pitfalls:
Assuming equivalences (“all poor are beggars”), or confusing necessary with sufficient conditions.

Final Answer:
If A is a beggar, then A is not rich.