Complementary Pair Some-No | Worksheet 7/10

Question 1

Statements: All birds are warm-blooded. No warm-blooded is a wild. Conclusions: I. Some wild are birds. II. No wild is a birds.

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

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

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

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 valuable are useful. No useful is a innovative. Conclusions: I. Some innovative are valuable. II. No innovative is a valuable.

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

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

Analytical Method:
All valuable are useful (A) + No useful is a innovative (E) = A + E = E = No valuable is a innovative
By conversion: No innovative 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 3

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

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

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

Analytical Method:
All accountants are architects (A) + No architects is a scientists (E) = A + E = E = No accountants is a scientists
By conversion: No scientists 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 4

Statements: All patterns are models. No models is a strategies. Conclusions: I. Some strategies are patterns. II. No strategies is a patterns.

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

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

Analytical Method:
All patterns are models (A) + No models is a strategies (E) = A + E = E = No patterns is a strategies
By conversion: No strategies 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 5

Statements: All accountants are scientists. No scientists 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 scientists" → Circle of accountants inside scientists
Step 2: "No scientists is a architects" → Circles of scientists and architects completely separate
Step 3: Since accountants is inside scientists, and scientists 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 scientists (A) + No scientists 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 6

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

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

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

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

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 reptiles are domestic. No domestic is a carnivores. Conclusions: I. Some carnivores are reptiles. II. No carnivores is a reptiles.

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

Analytical Method:
All reptiles are domestic (A) + No domestic is a carnivores (E) = A + E = E = No reptiles is a carnivores
By conversion: No carnivores 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 8

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

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

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

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

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 birds are fish. No fish is a invertebrates. Conclusions: I. Some invertebrates are birds. II. No invertebrates is a birds.

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

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

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

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

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

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

Analytical Method:
All reliable are accessible (A) + No accessible is a efficient (E) = A + E = E = No reliable is a efficient
By conversion: No efficient 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 systems are methods. No methods is a patterns. Conclusions: I. Some patterns are systems. II. No patterns is a systems.

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

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

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

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 diurnal are fish. No fish is a carnivores. Conclusions: I. Some carnivores are diurnal. II. No carnivores is a diurnal.

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

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

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

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

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

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

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

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

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

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

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

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 birds are carnivores. No carnivores is a invertebrates. Conclusions: I. Some invertebrates are birds. II. No invertebrates is a birds.

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

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

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

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 nocturnal are diurnal. No diurnal is a vertebrates. Conclusions: I. Some vertebrates are nocturnal. II. No vertebrates is a nocturnal.

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

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

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

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 omnivores are mammals. No mammals is a fish. Conclusions: I. Some fish are omnivores. II. No fish is a omnivores.

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

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

Analytical Method:
All omnivores are mammals (A) + No mammals is a fish (E) = A + E = E = No omnivores is a fish
By conversion: No fish 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 18

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

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

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

Analytical Method:
All principles are patterns (A) + No patterns is a models (E) = A + E = E = No principles is a models
By conversion: No models 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 19

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

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

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

Analytical Method:
All reliable are innovative (A) + No innovative is a essential (E) = A + E = E = No reliable is a essential
By conversion: No essential 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 20

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

Master Complementary Pair Some-No - Intermediate-Advanced Level Problems Complementary Pair Some-No INTERMEDIATE ADVANCED

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