Read the following statements and treat them as true, then decide which of the given conclusions logically follow. Statements: All swans are parrots. No parrot is a cuckoo. Conclusions: I. No swan is a cuckoo. II. All parrots are swans.

Difficulty: Easy

Correct Answer: Only conclusion I follows

Explanation:


Introduction / Context:
This is a standard two statement syllogism question involving three sets: swans, parrots, and cuckoos. You must determine which of the conclusions follow logically from the given statements. The statements define a subset relationship and a complete exclusion relationship. The challenge is to correctly propagate the exclusion from parrots to swans and to see whether there is any forced equivalence between parrots and swans.


Given Data / Assumptions:

  • Statement 1: All swans are parrots.
  • Statement 2: No parrot is a cuckoo.
  • Conclusion I: No swan is a cuckoo.
  • Conclusion II: All parrots are swans.
  • All statements are to be read as logically precise descriptions of the sets.


Concept / Approach:
When we say “All swans are parrots,” we are stating that the set of swans is contained inside the set of parrots. When we say “No parrot is a cuckoo,” we say that the sets parrots and cuckoos are disjoint. To determine whether a conclusion follows, we must ask whether it holds in all possible Venn diagrams that satisfy the premises. For Conclusion I, we test whether the disjointness between parrots and cuckoos transfers to swans. For Conclusion II, we test whether the subset relationship can be reversed.


Step-by-Step Solution:
Step 1: Represent the first statement: All swans are parrots. So the Swans set lies completely within the Parrots set. Step 2: Represent the second statement: No parrot is a cuckoo. This means the Parrots set and the Cuckoos set do not overlap at all. Step 3: Consider Conclusion I: “No swan is a cuckoo.” Since every swan is a parrot (from Statement 1), and no parrot is a cuckoo (from Statement 2), it is impossible for any swan to be a cuckoo. If a swan were a cuckoo, it would also be a parrot, contradicting Statement 2. Therefore, Swans ∩ Cuckoos is empty. Conclusion I is logically valid. Step 4: Now consider Conclusion II: “All parrots are swans.” This asserts that the Parrots set is contained inside the Swans set. However, the first statement only tells us that Swans is a subset of Parrots, not that they are equal. There might be parrots that are not swans. Step 5: Construct a counterexample for Conclusion II. Imagine a world with two birds: one swan and one non swan parrot. Let the swan be a parrot as well, satisfying “All swans are parrots.” Let the non swan parrot simply be a parrot that is not a swan. Also, let there be no cuckoos at all, so “No parrot is a cuckoo” is trivially true. In this arrangement, not all parrots are swans, because one parrot is not a swan. Thus Conclusion II does not necessarily follow.


Verification / Alternative check:
Using a Venn diagram, draw a large circle for Parrots. Inside it, draw a smaller circle for Swans. For Cuckoos, draw a separate circle that does not intersect Parrots at all. It is visually clear that no swan (inside Parrots) can intersect with Cuckoos, confirming Conclusion I. It is equally clear that Parrots is larger than Swans and need not be entirely inside Swans. There can be parrots outside the Swans circle, which invalidates Conclusion II as a universal claim.


Why Other Options Are Wrong:
Option a: “Only conclusion II follows” is incorrect because Conclusion II does not follow, while Conclusion I does. Option c: “Either conclusion I or conclusion II follows” is wrong because there is no either or situation; Conclusion I always follows, while Conclusion II does not. Option d: “Both conclusion I and conclusion II follow” is false because Conclusion II does not logically follow. Option e: “Neither conclusion I nor conclusion II follows” is incorrect since Conclusion I is clearly implied by the premises.


Common Pitfalls:
Learners sometimes misread “All swans are parrots” as “All parrots are swans,” which reverses the subset relationship. They also may think that if a set is a subset of another, they are automatically equal, which is not generally true. Always pay close attention to the direction of “all A are B” statements and remember that they do not guarantee the reverse unless explicitly stated.


Final Answer:
Only conclusion I follows.

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