Introduction / Context:
We must judge whether any of the conclusions is forced by the premises. Be careful: showing that a conclusion is “possible” is not enough; it must be necessary given the statements.
Given Data / Assumptions:
- No Rabbit is a Lion (R ∩ L = ∅).
- Some Horses are Lions (∃ H ∩ L).
- All Rabbits are Tables (R ⊆ T).
Concept / Approach:
- From R ⊆ T and R ∩ L = ∅, Rabbits are Tables that are non-Lions; this does not tell us whether other Tables might be Lions.
- Independence of Horses from Rabbits means we cannot infer overlap unless stated.
Step-by-Step Solution:
(I) “Some tables are lions.” Not necessary. Tables could include many non-rabbit items, but the premises do not force any Table to be a Lion. A compliant model can keep Tables disjoint from Lions except for Horses, which need not be Tables.(II) “Some horses are rabbits.” No link is given between Horses and Rabbits; the overlap is not compelled.(III) “No lion is a table.” Also not compelled. It is consistent that some non-rabbit Tables could be Lions, though not required. Hence this universal negative does not necessarily follow.
Verification / Alternative check:
Construct a model where Tables = Rabbits only. Then Tables and Lions are disjoint, satisfying premises; (I) is false, (III) true in this model, but a different model could add extra Tables overlapping Lions without contradicting premises, making (III) false. Since conclusions vary across valid models, none is necessary.
Why Other Options Are Wrong:
Any option selecting I, II, or III treats a merely possible relation as necessary.
Common Pitfalls:
Assuming “All Rabbits are Tables” implies “All Tables are Rabbits.” It does not; subset is one-way.
Final Answer:
None follows
Discussion & Comments