Complementary Pair Some-No | Worksheet 5/10

Question 1

Statements: All durable are beautiful. No beautiful is a useful. Conclusions: I. Some useful are durable. II. No useful is a durable.

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

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

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

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 sustainable are beautiful. No beautiful is a innovative. Conclusions: I. Some innovative are sustainable. II. No innovative is a sustainable.

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

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

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

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 entrepreneurs are pilots. No pilots is a doctors. Conclusions: I. Some doctors are entrepreneurs. II. No doctors is a entrepreneurs.

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

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

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

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 efficient are reliable. No reliable is a useful. Conclusions: I. Some useful are efficient. II. No useful is a efficient.

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

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

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

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 furniture are machines. No machines is a equipment. Conclusions: I. Some equipment are furniture. II. No equipment is a furniture.

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

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

Analytical Method:
All furniture are machines (A) + No machines is a equipment (E) = A + E = E = No furniture is a equipment
By conversion: No equipment 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 6

Statements: All durable are innovative. No innovative is a reliable. Conclusions: I. Some reliable are durable. II. No reliable is a durable.

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

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

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

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 pilots are doctors. No doctors is a scientists. Conclusions: I. Some scientists are pilots. II. No scientists is a pilots.

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

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

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

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 beautiful are versatile. No versatile is a valuable. Conclusions: I. Some valuable are beautiful. II. No valuable is a beautiful.

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

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

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

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 accessible are durable. No durable is a innovative. Conclusions: I. Some innovative are accessible. II. No innovative is a accessible.

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

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

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

Question 10

Statements: All reliable are essential. No essential is a versatile. Conclusions: I. Some versatile are reliable. II. No versatile is a reliable.

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

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

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

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 vehicles are machines. No machines is a ornaments. Conclusions: I. Some ornaments are vehicles. II. No ornaments is a vehicles.

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

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

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

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 accountants are athletes. No athletes is a architects. Conclusions: I. Some architects are accountants. II. No architects is a accountants.

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

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

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

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 wild are warm-blooded. No warm-blooded is a domestic. Conclusions: I. Some domestic are wild. II. No domestic is a wild.

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

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

Analytical Method:
All wild are warm-blooded (A) + No warm-blooded is a domestic (E) = A + E = E = No wild is a domestic
By conversion: No domestic is a wild

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 structures are frameworks. No frameworks is a concepts. Conclusions: I. Some concepts are structures. II. No concepts is a structures.

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

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

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

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 efficient are sustainable. No sustainable is a rare. Conclusions: I. Some rare are efficient. II. No rare is a efficient.

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

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

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

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 athletes are pharmacists. No pharmacists is a doctors. Conclusions: I. Some doctors are athletes. II. No doctors is a athletes.

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

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

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

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 athletes are engineers. No engineers is a pilots. Conclusions: I. Some pilots are athletes. II. No pilots is a athletes.

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

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

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

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 cold-blooded are invertebrates. No invertebrates is a reptiles. Conclusions: I. Some reptiles are cold-blooded. II. No reptiles is a cold-blooded.

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

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

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

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 nocturnal. No nocturnal is a wild. Conclusions: I. Some wild are carnivores. II. No wild is a carnivores.

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

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

Analytical Method:
All carnivores are nocturnal (A) + No nocturnal is a wild (E) = A + E = E = No carnivores is a wild
By conversion: No wild 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 doctors are managers. No managers is a entrepreneurs. Conclusions: I. Some entrepreneurs are doctors. II. No entrepreneurs is a doctors.

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

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

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

Complementary Pair Some-No - Intermediate Level: tricky scenarios handling Complementary Pair Some-No INTERMEDIATE

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