Introduction / Context:
Here we have one subset relationship and one universal negative, plus a particular fact about tigers and toys. The aim is to see whether any of the stated consequences must follow.
Given Data / Assumptions:
- B ⊆ W (all buildings are windows)
- Toy ∩ B = ∅ (no toy is a building)
- ∃ element in Tiger ∩ Toy (some tigers are toys)
Concept / Approach:
The particular fact ties tigers to toys, and the universal negative separates toys from buildings. The subset only says buildings lie within windows, not that all windows are buildings.
Step-by-Step Solution:
I: Some tigers are buildings. False, because those tigers picked from Tiger ∩ Toy are toys, and toys are not buildings.II: Some windows are tigers. Not guaranteed. We know nothing that links windows to toys or tigers; windows may exist outside buildings, but no necessary overlap with tigers is given.III: All toys are tigers. False; we only know some tigers are toys, not that all toys are tigers.IV: Some windows are toys. Not necessary because toys are disjoint from buildings, and buildings are the only guaranteed subset of windows; toys may or may not be windows via other routes, which are not specified.
Verification / Alternative check:
A model with no overlap between windows (outside buildings) and toys satisfies all premises and makes II and IV false, confirming that none of the conclusions must follow.
Why Other Options Are Wrong:
B, C, D, E each assert at least one conclusion that is not necessary under the premises.
Common Pitfalls:
Assuming all windows are buildings (converse error); assuming toys must connect to windows or buildings beyond what is stated.
Final Answer:
None follows
Discussion & Comments