Syllogism – Universals with a negative and an unrelated particular: Statements: All benches are cots. No cot is a lamp. Some lamps are candles. Conclusions: I) Some cots are benches. II) Some candles are cots. Choose the option that states what necessarily follows.

Introduction / Context:
This item checks two common traps: (1) reading existence from a universal statement, and (2) projecting an unrelated particular onto a set that is explicitly disjoint. Careful set reasoning avoids both errors.

Given Data / Assumptions:

• All Benches are Cots (B ⊆ C).
• No Cot is a Lamp (C ∩ L = ∅).
• Some Lamps are Candles (∃ L ∩ Candles).
• No premise asserts that Benches actually exist; there is no 'some B' clause.

Concept / Approach:
Conclusion I, 'Some cots are benches', requires existence of at least one Bench. A universal premise 'All B are C' is satisfied even if B is empty; therefore we cannot infer 'Some'. Conclusion II attempts to connect Candles to Cots via Lamps, but we know C and L are disjoint, and nothing links Candles to C except through L.

Step-by-Step Solution:
C1: If B = ∅, Premise 1 remains true while 'Some C are B' is false. So I does not necessarily follow.C2: From C ∩ L = ∅ and 'Some L are Candles', any element in L∩Candles is automatically not in C. Without another premise bringing Candles into C outside of L, we cannot force Candles ∩ C ≠ ∅.

Verification / Alternative check:
Model: Let C be a non-empty set, B = ∅, L disjoint from C, and let some elements of L be Candles. All premises hold. Yet C1 fails (no C that is B exists) and C2 fails (Candles inside L cannot be C). Hence neither conclusion is necessary.

Why Other Options Are Wrong:

• Only I follows / Only II follows / Both follow / Either follows: each is contradicted by the countermodel where B is empty and Candles live entirely within Lamps disjoint from Cots.

Common Pitfalls:
Assuming universals imply existence (they do not) and forgetting that an explicit 'No C is L' blocks any path from Lamps to Cots.

Final Answer:
Neither Conclusion I nor II follows.