Syllogism — Boys, men, and black (complements): Statements: • Some boys are men. • No man is black. Conclusions: I. Some boys are not black. II. Some men are boys.

Introduction / Context:We combine a particular inclusion with a universal negative to infer a particular negative and recognize an equivalent restatement.

Given Data / Assumptions:

• Some Boys are Men (∃ Boy ∩ Man).
• No Man is Black (Man ⊆ not Black).

Concept / Approach:The Boys who are Men are not Black, establishing I. Since “Some Boys are Men” is equivalent to “Some Men are Boys,” II also follows.

Step-by-Step:1) From ∃ (Boy ∩ Man) and Man ⊆ (not Black), infer ∃ (Boy ∩ not Black) — that is, Some boys are not black (I).2) The same premise directly gives ∃ (Man ∩ Boy), which is II.

Why Other Options Are Wrong:Any option excluding either I or II ignores necessary consequences.

Final Answer:Both I and II follow.