Consider the following logical statements to be true and decide which conclusions can definitely be drawn from them. Statements: 1. All fish are tortoise. 2. No tortoise is a crocodile. Conclusions: I. No crocodile is a fish. II. No fish is a crocodile. Treat this as a standard statement and conclusion problem and choose the option that correctly identifies which conclusion or conclusions follow.

Difficulty: Easy

Correct Answer: Both conclusions I and II follow

Explanation:


Introduction / Context:
Here you must analyse two statements about fish, tortoise, and crocodiles and then check which of the given conclusions are logically forced. This is a standard example of combining “all” and “no” type statements to find which sets are disjoint.


Given Data / Assumptions:
Take the following as fully true.

  • Statement 1: All fish are tortoise.
  • Statement 2: No tortoise is a crocodile.
  • Conclusion I: No crocodile is a fish.
  • Conclusion II: No fish is a crocodile.


Concept / Approach:
“All fish are tortoise” means Fish is a subset of Tortoise. “No tortoise is a crocodile” means the Tortoise and Crocodile sets have no common elements. If every fish is inside Tortoise and Tortoise has no overlap with Crocodile, then Fish also has no overlap with Crocodile. We then express this disjoint relation in both possible word orders.


Step-by-Step Solution:

Step 1: From statement 1, every fish lies in the Tortoise set. There is no fish outside Tortoise. Step 2: From statement 2, Tortoise and Crocodile are disjoint sets. No animal can be both a tortoise and a crocodile. Step 3: Since all fish are inside the Tortoise set and the Tortoise set is completely separate from the Crocodile set, it is impossible for any fish to be a crocodile. So “No fish is a crocodile” is necessarily true and matches conclusion II. Step 4: If no fish is a crocodile, the same fact can also be stated as “No crocodile is a fish.” The phrase “No A is B” automatically means “No B is A.” So conclusion I is also necessarily true.


Verification / Alternative check:
Draw a large circle for Tortoise. Inside it draw a smaller circle for Fish. Draw a separate circle for Crocodile completely outside Tortoise. There is no overlap between Fish and Crocodile since Fish is entirely within Tortoise and Tortoise does not meet Crocodile. The disjointness between Fish and Crocodile can be described in both directions, reinforcing both conclusions.


Why Other Options Are Wrong:
Option A says only conclusion I follows, ignoring that conclusion II is the same relation expressed with the sets reversed. Option B says only conclusion II follows and similarly ignores the equivalent restatement in conclusion I. Option D claims neither follows, which conflicts with the clearly implied disjointness between Fish and Crocodile.


Common Pitfalls:
Many learners forget that “No A is B” is symmetric. If no fish is a crocodile, then automatically no crocodile is a fish. The exam may include both forms as separate conclusions to test this understanding.


Final Answer:
Both conclusions I and II necessarily follow from the statements. Hence, the correct answer is “Both conclusions I and II follow.”

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