Statements: • All bulbs are wires. • No wire is a cable. • Some cables are brushes. • All brushes are paints. Conclusions: I. Some paints are cables. II. Some wires are bulbs. III. Some brushes are wires. IV. Some cables are bulbs. Choose the option that must follow.

Introduction / Context:This question combines a universal inclusion, a universal exclusion, and an existential that is pushed forward by another universal. We check which intersections are compelled.

Given Data / Assumptions:

• Bulbs ⊆ Wires.
• Wires ∩ Cables = ∅.
• ∃c_b ∈ Cables ∩ Brushes.
• Brushes ⊆ Paints.

Concept / Approach:From c_b ∈ Brushes and Brushes ⊆ Paints, we obtain Paints ∩ Cables ≠ ∅ (I true). II requires existence of Bulbs, which is not given by “All bulbs are wires.” III and IV contradict or overreach given the exclusion: brushes need not be wires, and bulbs cannot be cables because bulbs are wires and wires are disjoint from cables.

Step-by-Step Solution:• I: Guaranteed by pushing c_b through the universal inclusion to Paints.• II: “Some wires are bulbs” needs a bulb to exist; not stated.• III: No link wires↔brushes is provided.• IV: Impossible because Bulbs ⊆ Wires and Wires ∩ Cables = ∅.

Verification / Alternative check:Let there be cables that are brushes; let there be no bulbs at all. Premises hold; I is true; II–IV fail.

Why Other Options Are Wrong:They add existence or overlap that is not supported, or contradict the exclusion.

Common Pitfalls:Assuming existence from a universal statement.

Final Answer:Only I follows.