Syllogism – Chains of inclusion across three sets Premises: 1) All branches are flowers. 2) All flowers are leaves. Conclusions to test: I) All branches are leaves. II) All leaves are branches. III) All flowers are branches. IV) Some leaves are branches.

Difficulty: Easy

Correct Answer: Only I and IV follow

Explanation:


Introduction / Context:
Syllogism questions with three terms often require chaining universal statements. Here, “All branches are flowers” and “All flowers are leaves” must be combined to check which conclusions necessarily hold. We also consider whether a particular (“some”) conclusion is justified given the premises and typical test conventions.


Given Data / Assumptions:

  • B = set of branches.
  • F = set of flowers.
  • L = set of leaves.
  • Premises: B ⊆ F and F ⊆ L.


Concept / Approach:
From subset chaining, B ⊆ L (transitivity). Claims reversing the subset (like “All leaves are branches”) are invalid. Whether we can state “Some leaves are branches” typically depends on whether B is non-empty. Most exam conventions assume the subject class exists, allowing a valid particular inference from the established inclusion.


Step-by-Step Solution:

From B ⊆ F and F ⊆ L, derive B ⊆ L. Thus Conclusion I is true.Conclusion II (L ⊆ B) reverses inclusion; not supported.Conclusion III (F ⊆ B) also reverses; not supported.Conclusion IV: If at least one branch exists, that element is a leaf; hence some leaves are branches—accepted under standard test assumptions.


Verification / Alternative check:

Venn diagram check: B inside F inside L supports I. The existence of any B point inside L supports IV. No configuration supports II or III.


Why Other Options Are Wrong:

A: Rejects I despite clear transitivity.C: Endorses the two false reversals.D: Asserts all four; II and III are wrong.


Common Pitfalls:

Mistaking “all A are B” for “all B are A,” and overlooking the standard existence assumption behind particular conclusions.


Final Answer:
Only I and IV follow

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