Syllogism and logical reasoning question on categorical statements: 'All fishes are grey in colour' and 'Some fishes are heavy' — determine which conclusions necessarily follow (All heavy fishes are grey; All light fishes are not grey)

Given data

• Premise 1: All fishes are grey in colour (Fish ⊆ Grey).
• Premise 2: Some fishes are heavy (∃ Fish ∩ Heavy).
• Conclusions to test:
  • I: All heavy fishes are grey.
  • II: All light fishes are not grey.

Concept/Approach (why this method)

Use standard categorical syllogism rules and set–subset reasoning. From 'All A are B', every member of A inherits property B. Particular existence ('Some') does not invert or extend universals to unrelated classes.

Step-by-Step calculation / logic1) From Premise 1, every fish is grey.2) 'Heavy fishes' are a subset of fishes (they are the fishes that are heavy).3) Therefore every heavy fish, being a fish, is grey ⇒ Conclusion I is necessarily true.4) 'Light fishes' are also fishes; since all fishes are grey, light fishes are grey, not 'not grey' ⇒ Conclusion II is false.

Verification/Alternative

Venn diagram: Put the entire Fish circle inside Grey. Any subcategory of Fish (Heavy-fish, Light-fish) lies inside Grey; hence I holds and II contradicts the diagram.

Common pitfalls

• Misreading 'All fishes are grey' as 'Only fishes are grey' (not stated).
• Assuming 'light' excludes 'grey'; colour and weight are independent attributes.

Final AnswerOnly conclusion I follows.