Syllogism — Determine which conclusions necessarily follow: Statements: • All fish are tortoises. • No tortoise is a crocodile. Conclusions: I. No crocodile is a fish. II. No fish is a crocodile.

Introduction / Context:This is a standard chain with one universal affirmative and one universal negative. We must test two logically equivalent rephrasings regarding the relationship between crocodiles and fish.

Given Data / Assumptions:

• All Fish ⊆ Tortoise.
• No Tortoise is a Crocodile (Tortoise ∩ Crocodile = ∅).

Concept / Approach:If set A is contained in set B, and B is disjoint from set C, then A is also disjoint from C. Equivalently: All Fish are not-Crocodiles; therefore, no Crocodile is Fish and no Fish is Crocodile.

Step-by-Step Solution:1) Fish ⊆ Tortoise.2) Tortoise ∩ Crocodile = ∅.3) Hence Fish ∩ Crocodile = ∅ (Fish cannot intersect a set that is already disjoint from all of Tortoise).4) From disjointness, both “No crocodile is a fish” and “No fish is a crocodile” are necessarily true.

Verification / Alternative check:Draw two circles Fish inside Tortoise, and a third circle Crocodile separate from Tortoise. There is no overlap of Fish with Crocodile, proving both conclusions.

Why Other Options Are Wrong:Any choice that keeps only one conclusion ignores the symmetry of “no A is B.”

Common Pitfalls:Missing that conclusions I and II are simply converse expressions of the same empty intersection.

Final Answer:Both conclusions I and II follow.