Syllogism — Premises: (a) All frogs are tortoises. (b) No tortoise is a crocodile. Conclusions: I) No crocodile is a frog. II) No frog is a crocodile.
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AOnly I follows
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BOnly II follows
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CBoth I and II follow
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DNeither I nor II follows
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ENone of these
Answer
Correct Answer: Both I and II follow
Explanation
Introduction / Context:We combine a universal inclusion with a universal exclusion and test equivalent ways to state the same separation.
Given Data / Assumptions:
- Frogs ⊆ Tortoises.
- Tortoises ∩ Crocodiles = ∅.
Concept / Approach:If all frogs are tortoises and no tortoise is a crocodile, then frogs share the same exclusion from crocodiles. Statements I and II are equivalent rephrasings of that separation.
Step-by-Step Solution:
Step 1: Substitute Frogs within Tortoises: any frog is a tortoise.Step 2: From (b), that tortoise cannot be a crocodile.Step 3: Therefore no frog is a crocodile, and equivalently no crocodile is a frog.Verification / Alternative check:Venn diagram: Frogs inside Tortoises; Tortoises disjoint from Crocodiles; hence Frogs disjoint from Crocodiles.
Why Other Options Are Wrong:Any option denying either I or II conflicts with the chain of inclusion and exclusion.
Common Pitfalls:Missing that I and II are logically equivalent statements of disjointness.
Final Answer:Both I and II follow.