Complementary negatives with a subset: Using 'All fish are tortoise' and 'No tortoise is a crocodile', determine whether the conclusions (I) 'No crocodile is a fish' and (II) 'No fish is a crocodile' both follow in standard syllogistic logic.
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Both I and II follow
Explanation
Given data
- Premise 1: Fish ⊆ Tortoise.
- Premise 2: Tortoise ∩ Crocodile = ∅.
- Conclusions: (I) No Crocodile is a Fish. (II) No Fish is a Crocodile.
Concept/Approach
If Fish are entirely within Tortoise and Tortoise and Crocodile are disjoint, then Fish and Crocodile are also disjoint. 'No S are P' is symmetric, so both formulations are true.
Step-by-step evaluation
1) Fish ⊆ Tortoise and Tortoise ∩ Crocodile = ∅ ⇒ Fish ∩ Crocodile = ∅.2) Therefore: (II) 'No Fish is a Crocodile' is true.3) Symmetrically: (I) 'No Crocodile is a Fish' is also true.Verification
Diagram Fish inside Tortoise; separate Crocodile set disjoint from Tortoise. No overlap with Fish either way; both conclusions stand.
Common pitfalls
- Believing only one of the symmetric 'No' statements holds; both are equivalent.
Final AnswerBoth I and II follow.