Question 1
Statements:
Some efficient are essential.
Some essential are rare.
Conclusions:
I. Some efficient are rare.
II. No efficient is a rare.
Venn Diagram Method:
Step 1: "Some efficient are essential" → efficient and essential overlap partially
Step 2: "Some essential are rare" → essential and rare overlap partially
Step 3: Multiple possibilities exist:
- efficient and rare may overlap (some A are C)
- efficient and rare may be separate (no A is C)
- efficient and rare may partially overlap
Analytical Method:
I + I combination gives NO definite conclusion.
The overlapping portions may or may not be the same part of essential.
Verification:
✗ Conclusion I: "Some efficient are rare" - NOT DEFINITE (possible but not certain)
✗ Conclusion II: "No efficient is a rare" - NOT DEFINITE (possible but not certain)
Answer: Neither conclusion I nor II follows
Step 1: "Some efficient are essential" → efficient and essential overlap partially
Step 2: "Some essential are rare" → essential and rare overlap partially
Step 3: Multiple possibilities exist:
- efficient and rare may overlap (some A are C)
- efficient and rare may be separate (no A is C)
- efficient and rare may partially overlap
Analytical Method:
I + I combination gives NO definite conclusion.
The overlapping portions may or may not be the same part of essential.
Verification:
✗ Conclusion I: "Some efficient are rare" - NOT DEFINITE (possible but not certain)
✗ Conclusion II: "No efficient is a rare" - NOT DEFINITE (possible but not certain)
Answer: Neither conclusion I nor II follows