Complementary Pair Some-No | Worksheet 9/10

Question 1

Statements: All ideas are strategies. No strategies is a frameworks. Conclusions: I. Some frameworks are ideas. II. No frameworks is a ideas.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some frameworks are ideas" and "No frameworks is a ideas"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All ideas are strategies" → Circle of ideas inside strategies
Step 2: "No strategies is a frameworks" → Circles of strategies and frameworks completely separate
Step 3: Since ideas is inside strategies, and strategies is separate from frameworks, then ideas is also separate from frameworks
Step 4: Result: "No frameworks is a ideas" is TRUE

Analytical Method:
All ideas are strategies (A) + No strategies is a frameworks (E) = A + E = E = No ideas is a frameworks
By conversion: No frameworks is a ideas

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 2

Statements: All omnivores are herbivores. No herbivores is a cold-blooded. Conclusions: I. Some cold-blooded are omnivores. II. No cold-blooded is a omnivores.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some cold-blooded are omnivores" and "No cold-blooded is a omnivores"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All omnivores are herbivores" → Circle of omnivores inside herbivores
Step 2: "No herbivores is a cold-blooded" → Circles of herbivores and cold-blooded completely separate
Step 3: Since omnivores is inside herbivores, and herbivores is separate from cold-blooded, then omnivores is also separate from cold-blooded
Step 4: Result: "No cold-blooded is a omnivores" is TRUE

Analytical Method:
All omnivores are herbivores (A) + No herbivores is a cold-blooded (E) = A + E = E = No omnivores is a cold-blooded
By conversion: No cold-blooded is a omnivores

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 3

Statements: All pharmacists are writers. No writers is a entrepreneurs. Conclusions: I. Some entrepreneurs are pharmacists. II. No entrepreneurs is a pharmacists.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some entrepreneurs are pharmacists" and "No entrepreneurs is a pharmacists"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All pharmacists are writers" → Circle of pharmacists inside writers
Step 2: "No writers is a entrepreneurs" → Circles of writers and entrepreneurs completely separate
Step 3: Since pharmacists is inside writers, and writers is separate from entrepreneurs, then pharmacists is also separate from entrepreneurs
Step 4: Result: "No entrepreneurs is a pharmacists" is TRUE

Analytical Method:
All pharmacists are writers (A) + No writers is a entrepreneurs (E) = A + E = E = No pharmacists is a entrepreneurs
By conversion: No entrepreneurs is a pharmacists

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 4

Statements: All equipment are devices. No devices is a vehicles. Conclusions: I. Some vehicles are equipment. II. No vehicles is a equipment.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some vehicles are equipment" and "No vehicles is a equipment"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All equipment are devices" → Circle of equipment inside devices
Step 2: "No devices is a vehicles" → Circles of devices and vehicles completely separate
Step 3: Since equipment is inside devices, and devices is separate from vehicles, then equipment is also separate from vehicles
Step 4: Result: "No vehicles is a equipment" is TRUE

Analytical Method:
All equipment are devices (A) + No devices is a vehicles (E) = A + E = E = No equipment is a vehicles
By conversion: No vehicles is a equipment

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 5

Statements: All strategies are methods. No methods is a theories. Conclusions: I. Some theories are strategies. II. No theories is a strategies.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some theories are strategies" and "No theories is a strategies"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All strategies are methods" → Circle of strategies inside methods
Step 2: "No methods is a theories" → Circles of methods and theories completely separate
Step 3: Since strategies is inside methods, and methods is separate from theories, then strategies is also separate from theories
Step 4: Result: "No theories is a strategies" is TRUE

Analytical Method:
All strategies are methods (A) + No methods is a theories (E) = A + E = E = No strategies is a theories
By conversion: No theories is a strategies

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 6

Statements: All fish are amphibians. No amphibians is a vertebrates. Conclusions: I. Some vertebrates are fish. II. No vertebrates is a fish.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some vertebrates are fish" and "No vertebrates is a fish"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All fish are amphibians" → Circle of fish inside amphibians
Step 2: "No amphibians is a vertebrates" → Circles of amphibians and vertebrates completely separate
Step 3: Since fish is inside amphibians, and amphibians is separate from vertebrates, then fish is also separate from vertebrates
Step 4: Result: "No vertebrates is a fish" is TRUE

Analytical Method:
All fish are amphibians (A) + No amphibians is a vertebrates (E) = A + E = E = No fish is a vertebrates
By conversion: No vertebrates is a fish

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 7

Statements: All useful are rare. No rare is a valuable. Conclusions: I. Some valuable are useful. II. No valuable is a useful.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some valuable are useful" and "No valuable is a useful"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All useful are rare" → Circle of useful inside rare
Step 2: "No rare is a valuable" → Circles of rare and valuable completely separate
Step 3: Since useful is inside rare, and rare is separate from valuable, then useful is also separate from valuable
Step 4: Result: "No valuable is a useful" is TRUE

Analytical Method:
All useful are rare (A) + No rare is a valuable (E) = A + E = E = No useful is a valuable
By conversion: No valuable is a useful

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 8

Statements: All doctors are scientists. No scientists is a musicians. Conclusions: I. Some musicians are doctors. II. No musicians is a doctors.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some musicians are doctors" and "No musicians is a doctors"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All doctors are scientists" → Circle of doctors inside scientists
Step 2: "No scientists is a musicians" → Circles of scientists and musicians completely separate
Step 3: Since doctors is inside scientists, and scientists is separate from musicians, then doctors is also separate from musicians
Step 4: Result: "No musicians is a doctors" is TRUE

Analytical Method:
All doctors are scientists (A) + No scientists is a musicians (E) = A + E = E = No doctors is a musicians
By conversion: No musicians is a doctors

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 9

Statements: All engineers are architects. No architects is a managers. Conclusions: I. Some managers are engineers. II. No managers is a engineers.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some managers are engineers" and "No managers is a engineers"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All engineers are architects" → Circle of engineers inside architects
Step 2: "No architects is a managers" → Circles of architects and managers completely separate
Step 3: Since engineers is inside architects, and architects is separate from managers, then engineers is also separate from managers
Step 4: Result: "No managers is a engineers" is TRUE

Analytical Method:
All engineers are architects (A) + No architects is a managers (E) = A + E = E = No engineers is a managers
By conversion: No managers is a engineers

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 10

Statements: All architects are artists. No artists is a writers. Conclusions: I. Some writers are architects. II. No writers is a architects.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some writers are architects" and "No writers is a architects"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All architects are artists" → Circle of architects inside artists
Step 2: "No artists is a writers" → Circles of artists and writers completely separate
Step 3: Since architects is inside artists, and artists is separate from writers, then architects is also separate from writers
Step 4: Result: "No writers is a architects" is TRUE

Analytical Method:
All architects are artists (A) + No artists is a writers (E) = A + E = E = No architects is a writers
By conversion: No writers is a architects

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 11

Statements: All valuable are sustainable. No sustainable is a versatile. Conclusions: I. Some versatile are valuable. II. No versatile is a valuable.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some versatile are valuable" and "No versatile is a valuable"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All valuable are sustainable" → Circle of valuable inside sustainable
Step 2: "No sustainable is a versatile" → Circles of sustainable and versatile completely separate
Step 3: Since valuable is inside sustainable, and sustainable is separate from versatile, then valuable is also separate from versatile
Step 4: Result: "No versatile is a valuable" is TRUE

Analytical Method:
All valuable are sustainable (A) + No sustainable is a versatile (E) = A + E = E = No valuable is a versatile
By conversion: No versatile is a valuable

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 12

Statements: All furniture are devices. No devices is a electronics. Conclusions: I. Some electronics are furniture. II. No electronics is a furniture.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some electronics are furniture" and "No electronics is a furniture"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All furniture are devices" → Circle of furniture inside devices
Step 2: "No devices is a electronics" → Circles of devices and electronics completely separate
Step 3: Since furniture is inside devices, and devices is separate from electronics, then furniture is also separate from electronics
Step 4: Result: "No electronics is a furniture" is TRUE

Analytical Method:
All furniture are devices (A) + No devices is a electronics (E) = A + E = E = No furniture is a electronics
By conversion: No electronics is a furniture

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 13

Statements: All equipment are tools. No tools is a gadgets. Conclusions: I. Some gadgets are equipment. II. No gadgets is a equipment.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some gadgets are equipment" and "No gadgets is a equipment"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All equipment are tools" → Circle of equipment inside tools
Step 2: "No tools is a gadgets" → Circles of tools and gadgets completely separate
Step 3: Since equipment is inside tools, and tools is separate from gadgets, then equipment is also separate from gadgets
Step 4: Result: "No gadgets is a equipment" is TRUE

Analytical Method:
All equipment are tools (A) + No tools is a gadgets (E) = A + E = E = No equipment is a gadgets
By conversion: No gadgets is a equipment

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 14

Statements: All electronics are instruments. No instruments is a ornaments. Conclusions: I. Some ornaments are electronics. II. No ornaments is a electronics.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some ornaments are electronics" and "No ornaments is a electronics"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All electronics are instruments" → Circle of electronics inside instruments
Step 2: "No instruments is a ornaments" → Circles of instruments and ornaments completely separate
Step 3: Since electronics is inside instruments, and instruments is separate from ornaments, then electronics is also separate from ornaments
Step 4: Result: "No ornaments is a electronics" is TRUE

Analytical Method:
All electronics are instruments (A) + No instruments is a ornaments (E) = A + E = E = No electronics is a ornaments
By conversion: No ornaments is a electronics

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 15

Statements: All versatile are beautiful. No beautiful is a accessible. Conclusions: I. Some accessible are versatile. II. No accessible is a versatile.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some accessible are versatile" and "No accessible is a versatile"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All versatile are beautiful" → Circle of versatile inside beautiful
Step 2: "No beautiful is a accessible" → Circles of beautiful and accessible completely separate
Step 3: Since versatile is inside beautiful, and beautiful is separate from accessible, then versatile is also separate from accessible
Step 4: Result: "No accessible is a versatile" is TRUE

Analytical Method:
All versatile are beautiful (A) + No beautiful is a accessible (E) = A + E = E = No versatile is a accessible
By conversion: No accessible is a versatile

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 16

Statements: All invertebrates are fish. No fish is a vertebrates. Conclusions: I. Some vertebrates are invertebrates. II. No vertebrates is a invertebrates.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some vertebrates are invertebrates" and "No vertebrates is a invertebrates"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All invertebrates are fish" → Circle of invertebrates inside fish
Step 2: "No fish is a vertebrates" → Circles of fish and vertebrates completely separate
Step 3: Since invertebrates is inside fish, and fish is separate from vertebrates, then invertebrates is also separate from vertebrates
Step 4: Result: "No vertebrates is a invertebrates" is TRUE

Analytical Method:
All invertebrates are fish (A) + No fish is a vertebrates (E) = A + E = E = No invertebrates is a vertebrates
By conversion: No vertebrates is a invertebrates

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 17

Statements: All carnivores are mammals. No mammals is a domestic. Conclusions: I. Some domestic are carnivores. II. No domestic is a carnivores.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some domestic are carnivores" and "No domestic is a carnivores"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All carnivores are mammals" → Circle of carnivores inside mammals
Step 2: "No mammals is a domestic" → Circles of mammals and domestic completely separate
Step 3: Since carnivores is inside mammals, and mammals is separate from domestic, then carnivores is also separate from domestic
Step 4: Result: "No domestic is a carnivores" is TRUE

Analytical Method:
All carnivores are mammals (A) + No mammals is a domestic (E) = A + E = E = No carnivores is a domestic
By conversion: No domestic is a carnivores

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 18

Statements: All reptiles are domestic. No domestic is a invertebrates. Conclusions: I. Some invertebrates are reptiles. II. No invertebrates is a reptiles.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some invertebrates are reptiles" and "No invertebrates is a reptiles"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All reptiles are domestic" → Circle of reptiles inside domestic
Step 2: "No domestic is a invertebrates" → Circles of domestic and invertebrates completely separate
Step 3: Since reptiles is inside domestic, and domestic is separate from invertebrates, then reptiles is also separate from invertebrates
Step 4: Result: "No invertebrates is a reptiles" is TRUE

Analytical Method:
All reptiles are domestic (A) + No domestic is a invertebrates (E) = A + E = E = No reptiles is a invertebrates
By conversion: No invertebrates is a reptiles

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 19

Statements: All carnivores are domestic. No domestic is a invertebrates. Conclusions: I. Some invertebrates are carnivores. II. No invertebrates is a carnivores.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some invertebrates are carnivores" and "No invertebrates is a carnivores"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All carnivores are domestic" → Circle of carnivores inside domestic
Step 2: "No domestic is a invertebrates" → Circles of domestic and invertebrates completely separate
Step 3: Since carnivores is inside domestic, and domestic is separate from invertebrates, then carnivores is also separate from invertebrates
Step 4: Result: "No invertebrates is a carnivores" is TRUE

Analytical Method:
All carnivores are domestic (A) + No domestic is a invertebrates (E) = A + E = E = No carnivores is a invertebrates
By conversion: No invertebrates is a carnivores

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Question 20

Statements: All accessible are sustainable. No sustainable is a durable. Conclusions: I. Some durable are accessible. II. No durable is a accessible.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some durable are accessible" and "No durable is a accessible"
These are opposite statements - at least one MUST be true.

Venn Diagram Method:
Step 1: "All accessible are sustainable" → Circle of accessible inside sustainable
Step 2: "No sustainable is a durable" → Circles of sustainable and durable completely separate
Step 3: Since accessible is inside sustainable, and sustainable is separate from durable, then accessible is also separate from durable
Step 4: Result: "No durable is a accessible" is TRUE

Analytical Method:
All accessible are sustainable (A) + No sustainable is a durable (E) = A + E = E = No accessible is a durable
By conversion: No durable is a accessible

Either-Or Case:
Since the conclusions form a complementary pair and one is definitely true, answer is "Either-Or".

Answer: Either conclusion I or II follows

Complementary Pair Some-No - Expert Level: conceptual clarity Complementary Pair Some-No EXPERT

What you'll learn in this worksheet: