Question 1
Statements:
Some innovative are essential.
All essential are useful.
No useful is a valuable.
All valuable are rare.
Conclusions:
I. Some innovative are useful.
II. No essential is a valuable.
III. Some rare are not useful.
Complex Multi-Statement Analysis:
Statement Chain:
1. Some innovative are essential → Partial overlap
2. All essential are useful → essential inside useful
3. No useful is a valuable → useful and valuable separate
4. All valuable are rare → valuable inside rare
Checking Each Conclusion:
✓ Conclusion I: "Some innovative are useful"
Some A are B (I) + All B are C (A) = I + A = I - FOLLOWS
✓ Conclusion II: "No essential is a valuable"
All B are C (A) + No C is D (E) = A + E = E - FOLLOWS
✓ Conclusion III: "Some rare are not useful"
All D are E (A) + No C is D (E, converted) = A + E = O* - FOLLOWS
Answer: All conclusions I, II and III follow
Statement Chain:
1. Some innovative are essential → Partial overlap
2. All essential are useful → essential inside useful
3. No useful is a valuable → useful and valuable separate
4. All valuable are rare → valuable inside rare
Checking Each Conclusion:
✓ Conclusion I: "Some innovative are useful"
Some A are B (I) + All B are C (A) = I + A = I - FOLLOWS
✓ Conclusion II: "No essential is a valuable"
All B are C (A) + No C is D (E) = A + E = E - FOLLOWS
✓ Conclusion III: "Some rare are not useful"
All D are E (A) + No C is D (E, converted) = A + E = O* - FOLLOWS
Answer: All conclusions I, II and III follow