Question 1
Statements:
Some devices are furniture.
All furniture are machines.
Conclusions:
I. All devices are machines.
II. Some devices are not machines.
Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All devices are machines" (A-type)
- "Some devices are not machines" (O-type)
These are opposite statements where at least one can be true.
Venn Diagram:
Step 1: "Some devices are furniture" → Partial overlap
Step 2: "All furniture are machines" → furniture inside machines
Step 3: The part of devices overlapping with furniture is definitely inside machines
Step 4: But we DON'T know about the rest of devices
Possible Cases:
Case 1: All of devices inside machines → Conclusion I true
Case 2: Some of devices outside machines → Conclusion II true
Either-Or Rule:
When conclusions form complementary pair "All" and "Some not", answer is "Either-Or".
Answer: Either conclusion I or II follows
Conclusions I and II form a complementary pair:
- "All devices are machines" (A-type)
- "Some devices are not machines" (O-type)
These are opposite statements where at least one can be true.
Venn Diagram:
Step 1: "Some devices are furniture" → Partial overlap
Step 2: "All furniture are machines" → furniture inside machines
Step 3: The part of devices overlapping with furniture is definitely inside machines
Step 4: But we DON'T know about the rest of devices
Possible Cases:
Case 1: All of devices inside machines → Conclusion I true
Case 2: Some of devices outside machines → Conclusion II true
Either-Or Rule:
When conclusions form complementary pair "All" and "Some not", answer is "Either-Or".
Answer: Either conclusion I or II follows