Syllogism — Tigers, Lions, Rabbits, Horses Statements: • Some tigers are lions. • Some lions are rabbits. • Some rabbits are horses. Conclusions: I. Some tigers are horses. II. Some rabbits are tigers. III. Some horses are lions. IV. All horses are.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This problem is a classic illustration that chaining several “some” statements does not justify concluding overlap among the first and last sets. Each “some” could refer to disjoint subgroups that never meet. Given Data / Assumptions: There exists Tiger ∩ Lion. There exists Lion ∩ Rabbit. There exists Rabbit ∩ Horse. Concept / Approach:With only particular affirmatives, intersections need not align. You cannot infer transitive overlap for “some.” Likewise, universal statements like “All horses are rabbits” cannot be derived from a single “some.” Step-by-Step Solution: Construct a countermodel: Let T∩L contain element a; L∩R contain element b (with b ≠ a); R∩H contain element c (c ≠ b, a). All premises hold. However, T∩H may be empty ⇒ Conclusion I fails.R∩T can be empty ⇒ Conclusion II fails.H∩L can be empty ⇒ Conclusion III fails.Only “some rabbits are horses” was given; “All horses are rabbits” is much stronger and not implied ⇒ Conclusion IV fails. Verification / Alternative check:The single countermodel suffices to show none of the four conclusions is logically necessary given the premises. Why Other Options Are Wrong: Any option listing I–IV assumes forced overlaps that the premises do not guarantee. Common Pitfalls:Illegally chaining “some” statements; confusing “some” with “all.” Final Answer:None follows

Syllogism — Tigers, Lions, Rabbits, Horses Statements: • Some tigers are lions. • Some lions are rabbits. • Some rabbits are horses. Conclusions: I. Some tigers are horses. II. Some rabbits are tigers. III. Some horses are lions. IV. All horses are rabbits.

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