Question 1
Statements:
Only rare are accessible.
All accessible are useful.
Conclusions:
I. All rare are useful.
II. Some useful are rare.
Understanding 'Only' Statement:
"Only rare are accessible" means "All accessible are rare" (reversal!)
Conversion:
Original: Only rare are accessible
Converted: All accessible are rare
Venn Diagram:
Step 1: "All accessible are rare" → accessible inside rare
Step 2: "All accessible are useful" → accessible inside useful
Step 3: accessible inside both rare and useful
Checking Conclusions:
✗ Conclusion I: "All rare are useful"
We only know accessible is inside both - rare could be larger - DOES NOT FOLLOW
✓ Conclusion II: "Some useful are rare"
All accessible are rare and all accessible are useful
The accessible portion is common to both - FOLLOWS
Answer: Only conclusion II follows
"Only rare are accessible" means "All accessible are rare" (reversal!)
Conversion:
Original: Only rare are accessible
Converted: All accessible are rare
Venn Diagram:
Step 1: "All accessible are rare" → accessible inside rare
Step 2: "All accessible are useful" → accessible inside useful
Step 3: accessible inside both rare and useful
Checking Conclusions:
✗ Conclusion I: "All rare are useful"
We only know accessible is inside both - rare could be larger - DOES NOT FOLLOW
✓ Conclusion II: "Some useful are rare"
All accessible are rare and all accessible are useful
The accessible portion is common to both - FOLLOWS
Answer: Only conclusion II follows