Complementary Pair All-SomeNot: Worksheet 6 - Intermediate-Advanced Practice Complementary Pair All-SomeNot INTERMEDIATE ADVANCED

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All vehicles are devices" (A-type)
- "Some vehicles are not devices" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some vehicles are appliances" → Partial overlap
Step 2: "All appliances are devices" → appliances inside devices
Step 3: The part of vehicles overlapping with appliances is definitely inside devices
Step 4: But we DON'T know about the rest of vehicles

Possible Cases:
Case 1: All of vehicles inside devices → Conclusion I true
Case 2: Some of vehicles outside devices → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All tools are instruments" (A-type)
- "Some tools are not instruments" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some tools are gadgets" → Partial overlap
Step 2: "All gadgets are instruments" → gadgets inside instruments
Step 3: The part of tools overlapping with gadgets is definitely inside instruments
Step 4: But we DON'T know about the rest of tools

Possible Cases:
Case 1: All of tools inside instruments → Conclusion I true
Case 2: Some of tools outside instruments → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All ornaments are machines" (A-type)
- "Some ornaments are not machines" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some ornaments are utensils" → Partial overlap
Step 2: "All utensils are machines" → utensils inside machines
Step 3: The part of ornaments overlapping with utensils is definitely inside machines
Step 4: But we DON'T know about the rest of ornaments

Possible Cases:
Case 1: All of ornaments inside machines → Conclusion I true
Case 2: Some of ornaments 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All teachers are scientists" (A-type)
- "Some teachers are not scientists" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some teachers are musicians" → Partial overlap
Step 2: "All musicians are scientists" → musicians inside scientists
Step 3: The part of teachers overlapping with musicians is definitely inside scientists
Step 4: But we DON'T know about the rest of teachers

Possible Cases:
Case 1: All of teachers inside scientists → Conclusion I true
Case 2: Some of teachers outside scientists → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All pilots are writers" (A-type)
- "Some pilots are not writers" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some pilots are athletes" → Partial overlap
Step 2: "All athletes are writers" → athletes inside writers
Step 3: The part of pilots overlapping with athletes is definitely inside writers
Step 4: But we DON'T know about the rest of pilots

Possible Cases:
Case 1: All of pilots inside writers → Conclusion I true
Case 2: Some of pilots outside writers → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All engineers are lawyers" (A-type)
- "Some engineers are not lawyers" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some engineers are pilots" → Partial overlap
Step 2: "All pilots are lawyers" → pilots inside lawyers
Step 3: The part of engineers overlapping with pilots is definitely inside lawyers
Step 4: But we DON'T know about the rest of engineers

Possible Cases:
Case 1: All of engineers inside lawyers → Conclusion I true
Case 2: Some of engineers outside lawyers → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All useful are reliable" (A-type)
- "Some useful are not reliable" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some useful are durable" → Partial overlap
Step 2: "All durable are reliable" → durable inside reliable
Step 3: The part of useful overlapping with durable is definitely inside reliable
Step 4: But we DON'T know about the rest of useful

Possible Cases:
Case 1: All of useful inside reliable → Conclusion I true
Case 2: Some of useful outside reliable → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All mammals are wild" (A-type)
- "Some mammals are not wild" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some mammals are birds" → Partial overlap
Step 2: "All birds are wild" → birds inside wild
Step 3: The part of mammals overlapping with birds is definitely inside wild
Step 4: But we DON'T know about the rest of mammals

Possible Cases:
Case 1: All of mammals inside wild → Conclusion I true
Case 2: Some of mammals outside wild → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All amphibians are warm-blooded" (A-type)
- "Some amphibians are not warm-blooded" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some amphibians are invertebrates" → Partial overlap
Step 2: "All invertebrates are warm-blooded" → invertebrates inside warm-blooded
Step 3: The part of amphibians overlapping with invertebrates is definitely inside warm-blooded
Step 4: But we DON'T know about the rest of amphibians

Possible Cases:
Case 1: All of amphibians inside warm-blooded → Conclusion I true
Case 2: Some of amphibians outside warm-blooded → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All valuable are sustainable" (A-type)
- "Some valuable are not sustainable" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some valuable are rare" → Partial overlap
Step 2: "All rare are sustainable" → rare inside sustainable
Step 3: The part of valuable overlapping with rare is definitely inside sustainable
Step 4: But we DON'T know about the rest of valuable

Possible Cases:
Case 1: All of valuable inside sustainable → Conclusion I true
Case 2: Some of valuable outside sustainable → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All versatile are rare" (A-type)
- "Some versatile are not rare" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some versatile are sustainable" → Partial overlap
Step 2: "All sustainable are rare" → sustainable inside rare
Step 3: The part of versatile overlapping with sustainable is definitely inside rare
Step 4: But we DON'T know about the rest of versatile

Possible Cases:
Case 1: All of versatile inside rare → Conclusion I true
Case 2: Some of versatile outside rare → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All domestic are birds" (A-type)
- "Some domestic are not birds" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some domestic are reptiles" → Partial overlap
Step 2: "All reptiles are birds" → reptiles inside birds
Step 3: The part of domestic overlapping with reptiles is definitely inside birds
Step 4: But we DON'T know about the rest of domestic

Possible Cases:
Case 1: All of domestic inside birds → Conclusion I true
Case 2: Some of domestic outside birds → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All methods are frameworks" (A-type)
- "Some methods are not frameworks" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some methods are principles" → Partial overlap
Step 2: "All principles are frameworks" → principles inside frameworks
Step 3: The part of methods overlapping with principles is definitely inside frameworks
Step 4: But we DON'T know about the rest of methods

Possible Cases:
Case 1: All of methods inside frameworks → Conclusion I true
Case 2: Some of methods outside frameworks → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All processes are concepts" (A-type)
- "Some processes are not concepts" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some processes are methods" → Partial overlap
Step 2: "All methods are concepts" → methods inside concepts
Step 3: The part of processes overlapping with methods is definitely inside concepts
Step 4: But we DON'T know about the rest of processes

Possible Cases:
Case 1: All of processes inside concepts → Conclusion I true
Case 2: Some of processes outside concepts → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All ornaments are instruments" (A-type)
- "Some ornaments are not instruments" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some ornaments are devices" → Partial overlap
Step 2: "All devices are instruments" → devices inside instruments
Step 3: The part of ornaments overlapping with devices is definitely inside instruments
Step 4: But we DON'T know about the rest of ornaments

Possible Cases:
Case 1: All of ornaments inside instruments → Conclusion I true
Case 2: Some of ornaments outside instruments → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All herbivores are vertebrates" (A-type)
- "Some herbivores are not vertebrates" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some herbivores are invertebrates" → Partial overlap
Step 2: "All invertebrates are vertebrates" → invertebrates inside vertebrates
Step 3: The part of herbivores overlapping with invertebrates is definitely inside vertebrates
Step 4: But we DON'T know about the rest of herbivores

Possible Cases:
Case 1: All of herbivores inside vertebrates → Conclusion I true
Case 2: Some of herbivores outside vertebrates → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All carnivores are domestic" (A-type)
- "Some carnivores are not domestic" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some carnivores are amphibians" → Partial overlap
Step 2: "All amphibians are domestic" → amphibians inside domestic
Step 3: The part of carnivores overlapping with amphibians is definitely inside domestic
Step 4: But we DON'T know about the rest of carnivores

Possible Cases:
Case 1: All of carnivores inside domestic → Conclusion I true
Case 2: Some of carnivores outside domestic → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All principles are ideas" (A-type)
- "Some principles are not ideas" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some principles are systems" → Partial overlap
Step 2: "All systems are ideas" → systems inside ideas
Step 3: The part of principles overlapping with systems is definitely inside ideas
Step 4: But we DON'T know about the rest of principles

Possible Cases:
Case 1: All of principles inside ideas → Conclusion I true
Case 2: Some of principles outside ideas → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All gadgets are furniture" (A-type)
- "Some gadgets are not furniture" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some gadgets are equipment" → Partial overlap
Step 2: "All equipment are furniture" → equipment inside furniture
Step 3: The part of gadgets overlapping with equipment is definitely inside furniture
Step 4: But we DON'T know about the rest of gadgets

Possible Cases:
Case 1: All of gadgets inside furniture → Conclusion I true
Case 2: Some of gadgets outside furniture → 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

Complementary Pair Analysis:
Conclusions I and II form a complementary pair:
- "All diurnal are wild" (A-type)
- "Some diurnal are not wild" (O-type)
These are opposite statements where at least one can be true.

Venn Diagram:
Step 1: "Some diurnal are domestic" → Partial overlap
Step 2: "All domestic are wild" → domestic inside wild
Step 3: The part of diurnal overlapping with domestic is definitely inside wild
Step 4: But we DON'T know about the rest of diurnal

Possible Cases:
Case 1: All of diurnal inside wild → Conclusion I true
Case 2: Some of diurnal outside wild → 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