Syllogism — Trees, Fruits, Stones, Rains Statements: • No tree is fruit. • All fruits are stones. • All stones are rains. Conclusions: I. No stone is tree. II. No rain is tree. III. Some rains are fruits. IV. Some rains are trees.
-
AOnly either II or III, and I follow
-
BNone follows
-
COnly either II or IV, and III follow
-
DAll follow
-
ENone of these
Answer
Correct Answer: None follows
Explanation
Introduction / Context:This question probes careful handling of universal negatives and inclusions, and whether they suffice to produce new universal negatives or particulars. The given information places Fruits inside Stones inside Rains, and separates Trees from Fruits only.
Given Data / Assumptions:
- Trees ∩ Fruits = ∅.
- Fruits ⊆ Stones ⊆ Rains.
Concept / Approach:From “No tree is fruit,” it does not follow that trees are disjoint from stones or rains, because stones contain items beyond fruits. Particular conclusions require existence which is not provided here for fruits (could be empty by the logic of classical syllogism without existential import).
Step-by-Step Solution:
I. “No stone is tree” — not implied. Non-fruit stones could overlap with trees; the premises do not forbid that.II. “No rain is tree” — not implied for the same reason; rains include more than fruits or stones that are fruits.III. “Some rains are fruits” — requires existence of fruits; existence is not guaranteed by the premises.IV. “Some rains are trees” — no information supports this overlap.Verification / Alternative check:Construct a model where the class Fruits is empty; all statements still hold, and then III is false. Also let some trees be within rains but outside stones; or outside rains altogether—either way, none of I–IV is forced.
Why Other Options Are Wrong:
- Any option claiming forced negatives about stones/rains and trees adds assumptions not present.
- “All follow” is far too strong.
Common Pitfalls:Assuming disjointness propagates upward to supersets; assuming existential import where none is given.
Final Answer:None follows