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