Complementary Pair Some-No | Worksheet 6/10

Question 1

Statements: All entrepreneurs are doctors. No doctors is a architects. Conclusions: I. Some architects are entrepreneurs. II. No architects is a entrepreneurs.

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

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

Analytical Method:
All entrepreneurs are doctors (A) + No doctors is a architects (E) = A + E = E = No entrepreneurs is a architects
By conversion: No architects 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 2

Statements: All entrepreneurs are artists. No artists 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 artists" → Circle of entrepreneurs inside artists
Step 2: "No artists is a doctors" → Circles of artists and doctors completely separate
Step 3: Since entrepreneurs is inside artists, and artists 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 artists (A) + No artists 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 3

Statements: All pharmacists are nurses. No nurses is a managers. Conclusions: I. Some managers are pharmacists. II. No managers is a pharmacists.

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

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

Analytical Method:
All pharmacists are nurses (A) + No nurses is a managers (E) = A + E = E = No pharmacists is a managers
By conversion: No managers 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 pharmacists are athletes. No athletes is a lawyers. Conclusions: I. Some lawyers are pharmacists. II. No lawyers is a pharmacists.

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

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

Analytical Method:
All pharmacists are athletes (A) + No athletes is a lawyers (E) = A + E = E = No pharmacists is a lawyers
By conversion: No lawyers 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 5

Statements: All furniture are machines. No machines is a ornaments. Conclusions: I. Some ornaments are furniture. II. No ornaments is a furniture.

Complementary Pair Concept:
Conclusions I and II form a complementary pair: "Some ornaments are furniture" and "No ornaments 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 ornaments" → Circles of machines and ornaments completely separate
Step 3: Since furniture is inside machines, and machines is separate from ornaments, then furniture is also separate from ornaments
Step 4: Result: "No ornaments is a furniture" is TRUE

Analytical Method:
All furniture are machines (A) + No machines is a ornaments (E) = A + E = E = No furniture is a ornaments
By conversion: No ornaments 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 vehicles are instruments. No instruments is a devices. Conclusions: I. Some devices are vehicles. II. No devices is a vehicles.

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

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

Analytical Method:
All vehicles are instruments (A) + No instruments is a devices (E) = A + E = E = No vehicles is a devices
By conversion: No devices 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 7

Statements: All athletes are entrepreneurs. No entrepreneurs is a musicians. Conclusions: I. Some musicians are athletes. II. No musicians is a athletes.

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

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

Analytical Method:
All athletes are entrepreneurs (A) + No entrepreneurs is a musicians (E) = A + E = E = No athletes is a musicians
By conversion: No musicians 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 8

Statements: All cold-blooded are fish. No fish is a vertebrates. Conclusions: I. Some vertebrates are cold-blooded. II. No vertebrates is a cold-blooded.

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

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

Analytical Method:
All cold-blooded are fish (A) + No fish is a vertebrates (E) = A + E = E = No cold-blooded is a vertebrates
By conversion: No vertebrates 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 9

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

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

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

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

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

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

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

Analytical Method:
All doctors are pilots (A) + No pilots is a nurses (E) = A + E = E = No doctors is a nurses
By conversion: No nurses 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 11

Statements: All doctors are architects. No architects is a athletes. Conclusions: I. Some athletes are doctors. II. No athletes is a doctors.

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

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

Analytical Method:
All doctors are architects (A) + No architects is a athletes (E) = A + E = E = No doctors is a athletes
By conversion: No athletes 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 12

Statements: All patterns are principles. No principles is a structures. Conclusions: I. Some structures are patterns. II. No structures is a patterns.

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

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

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

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

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

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

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

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 vertebrates are wild. No wild is a fish. Conclusions: I. Some fish are vertebrates. II. No fish is a vertebrates.

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

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

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

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 vehicles are equipment. No equipment is a electronics. Conclusions: I. Some electronics are vehicles. II. No electronics is a vehicles.

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

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

Analytical Method:
All vehicles are equipment (A) + No equipment is a electronics (E) = A + E = E = No vehicles is a electronics
By conversion: No electronics 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 16

Statements: All domestic are warm-blooded. No warm-blooded is a herbivores. Conclusions: I. Some herbivores are domestic. II. No herbivores is a domestic.

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

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

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

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 principles are structures. No structures is a methods. Conclusions: I. Some methods are principles. II. No methods is a principles.

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

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

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

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

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

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

Analytical Method:
All beautiful are valuable (A) + No valuable is a essential (E) = A + E = E = No beautiful is a essential
By conversion: No essential 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 19

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

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

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

Analytical Method:
All equipment are furniture (A) + No furniture is a devices (E) = A + E = E = No equipment is a devices
By conversion: No devices 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 20

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

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

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

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

Complementary Pair Some-No: Worksheet 6 - Intermediate-Advanced Practice Complementary Pair Some-No INTERMEDIATE ADVANCED

What you'll learn in this worksheet: