Syllogism with shared superset: 'All bags are cakes' and 'All lamps are cakes' — decide whether it necessarily follows that some lamps are bags or that no lamp is a bag (evaluate the valid either–or inference)

Given data

• Premise 1: All bags ⊆ cakes.
• Premise 2: All lamps ⊆ cakes.
• Conclusions:
  • I: Some lamps are bags.
  • II: No lamp is a bag.

Concept/Approach

Both sets (bags, lamps) are contained in the larger set (cakes). Their mutual relation is undetermined by the premises: they may overlap or be disjoint. In classical syllogism tests, such a pair forms a valid 'either–or' conclusion: exactly one of 'some overlap' or 'no overlap' must be true in any model, though we cannot say which.

Step-by-step reasoning
1) From the premises alone, both intersection and disjoint models are possible.2) Since I and II are mutually exclusive and together exhaustive, the correct inference form is 'Either I or II follows'.

Verification/Alternative

Model A (overlap): some lamps are bags ⇒ I true, II false. Model B (disjoint): no lamp is a bag ⇒ II true, I false. In all models, one (and only one) holds.

Common pitfalls

• Marking 'neither' because each individually is not necessary, forgetting the accepted either–or rule in such problems.

Final Answer
Either I or II follows.