Syllogism — Combine several categories; watch existence requirements Statements: • Some doctors are lawyers. • All teachers are lawyers. • Some engineers are lawyers. • All engineers are businessmen. Conclusions: I) Some teachers are doctors. II) Some businessmen are lawyers. III) Some businessmen are teachers. IV) Some lawyers are teachers. Select what must follow.

Introduction / Context:
Here multiple set relations appear together. The safe path is to identify conclusions supported by a single chain using the same existential witness, and to reject conclusions that require intersections not guaranteed by the premises.

Given Data / Assumptions:

• ∃x: x ∈ Doctors ∩ Lawyers.
• Teachers ⊆ Lawyers.
• ∃y: y ∈ Engineers ∩ Lawyers.
• Engineers ⊆ Businessmen.

Concept / Approach:
From “Some engineers are lawyers” and “All engineers are businessmen,” pick that same engineer as the witness; they are both a businessman and a lawyer. That confirms “Some businessmen are lawyers.” Intersections involving Teachers require existence of Teachers (not stated) and further overlap with Doctors or Businessmen (also not stated).

Step-by-Step Solution:

Verification / Alternative check:
Construct a model with engineers (hence businessmen) who are lawyers, some doctors who are lawyers, and zero teachers. All premises hold and only II is forced.

Why Other Options Are Wrong:
Any option including I, III, or IV assumes extra existence/overlap not ensured by the premises.

Common Pitfalls:
Assuming existence for a class mentioned only in a universal statement (“All teachers are lawyers”) and over-connecting different “some” statements.

Final Answer:
Only II follows.