Three Statement Standard | Final Worksheet (10/10)

Question 1

Statements: All utensils are gadgets. Some gadgets are electronics. No electronics is a furniture. Conclusions: I. Some utensils are not furniture. II. Some gadgets are not furniture. III. No furniture is a electronics.

Step-by-Step Analysis:

Statement 1: All utensils are gadgets → utensils inside gadgets
Statement 2: Some gadgets are electronics → gadgets and electronics overlap
Statement 3: No electronics is a furniture → electronics and furniture separate

Checking Conclusions:

✗ Conclusion I: "Some utensils are not furniture"
Cannot determine relationship between utensils and furniture - NOT PROVEN

✓ Conclusion II: "Some gadgets are not furniture"
Some gadgets are electronics (given) + No electronics is furniture (given)
Those gadgets which are electronics cannot be furniture - FOLLOWS

✓ Conclusion III: "No furniture is a electronics"
Conversion of "No electronics is a furniture" - FOLLOWS

Answer: Conclusions II and III follow

Question 2

Statements: All accessible are durable. Some durable are rare. No rare is a valuable. Conclusions: I. Some accessible are not valuable. II. Some durable are not valuable. III. No valuable is a rare.

Step-by-Step Analysis:

Statement 1: All accessible are durable → accessible inside durable
Statement 2: Some durable are rare → durable and rare overlap
Statement 3: No rare is a valuable → rare and valuable separate

Checking Conclusions:

✗ Conclusion I: "Some accessible are not valuable"
Cannot determine relationship between accessible and valuable - NOT PROVEN

✓ Conclusion II: "Some durable are not valuable"
Some durable are rare (given) + No rare is valuable (given)
Those durable which are rare cannot be valuable - FOLLOWS

✓ Conclusion III: "No valuable is a rare"
Conversion of "No rare is a valuable" - FOLLOWS

Answer: Conclusions II and III follow

Question 3

Statements: All teachers are scientists. Some scientists are lawyers. No lawyers is a artists. Conclusions: I. Some teachers are not artists. II. Some scientists are not artists. III. No artists is a lawyers.

Step-by-Step Analysis:

Statement 1: All teachers are scientists → teachers inside scientists
Statement 2: Some scientists are lawyers → scientists and lawyers overlap
Statement 3: No lawyers is a artists → lawyers and artists separate

Checking Conclusions:

✗ Conclusion I: "Some teachers are not artists"
Cannot determine relationship between teachers and artists - NOT PROVEN

✓ Conclusion II: "Some scientists are not artists"
Some scientists are lawyers (given) + No lawyers is artists (given)
Those scientists which are lawyers cannot be artists - FOLLOWS

✓ Conclusion III: "No artists is a lawyers"
Conversion of "No lawyers is a artists" - FOLLOWS

Answer: Conclusions II and III follow

Question 4

Statements: All tools are ornaments. Some ornaments are vehicles. No vehicles is a equipment. Conclusions: I. Some tools are not equipment. II. Some ornaments are not equipment. III. No equipment is a vehicles.

Step-by-Step Analysis:

Statement 1: All tools are ornaments → tools inside ornaments
Statement 2: Some ornaments are vehicles → ornaments and vehicles overlap
Statement 3: No vehicles is a equipment → vehicles and equipment separate

Checking Conclusions:

✗ Conclusion I: "Some tools are not equipment"
Cannot determine relationship between tools and equipment - NOT PROVEN

✓ Conclusion II: "Some ornaments are not equipment"
Some ornaments are vehicles (given) + No vehicles is equipment (given)
Those ornaments which are vehicles cannot be equipment - FOLLOWS

✓ Conclusion III: "No equipment is a vehicles"
Conversion of "No vehicles is a equipment" - FOLLOWS

Answer: Conclusions II and III follow

Question 5

Statements: All ideas are models. Some models are frameworks. No frameworks is a systems. Conclusions: I. Some ideas are not systems. II. Some models are not systems. III. No systems is a frameworks.

Step-by-Step Analysis:

Statement 1: All ideas are models → ideas inside models
Statement 2: Some models are frameworks → models and frameworks overlap
Statement 3: No frameworks is a systems → frameworks and systems separate

Checking Conclusions:

✗ Conclusion I: "Some ideas are not systems"
Cannot determine relationship between ideas and systems - NOT PROVEN

✓ Conclusion II: "Some models are not systems"
Some models are frameworks (given) + No frameworks is systems (given)
Those models which are frameworks cannot be systems - FOLLOWS

✓ Conclusion III: "No systems is a frameworks"
Conversion of "No frameworks is a systems" - FOLLOWS

Answer: Conclusions II and III follow

Question 6

Statements: All vehicles are devices. Some devices are instruments. No instruments is a furniture. Conclusions: I. Some vehicles are not furniture. II. Some devices are not furniture. III. No furniture is a instruments.

Step-by-Step Analysis:

Statement 1: All vehicles are devices → vehicles inside devices
Statement 2: Some devices are instruments → devices and instruments overlap
Statement 3: No instruments is a furniture → instruments and furniture separate

Checking Conclusions:

✗ Conclusion I: "Some vehicles are not furniture"
Cannot determine relationship between vehicles and furniture - NOT PROVEN

✓ Conclusion II: "Some devices are not furniture"
Some devices are instruments (given) + No instruments is furniture (given)
Those devices which are instruments cannot be furniture - FOLLOWS

✓ Conclusion III: "No furniture is a instruments"
Conversion of "No instruments is a furniture" - FOLLOWS

Answer: Conclusions II and III follow

Question 7

Statements: All architects are doctors. Some doctors are musicians. No musicians is a scientists. Conclusions: I. Some architects are not scientists. II. Some doctors are not scientists. III. No scientists is a musicians.

Step-by-Step Analysis:

Statement 1: All architects are doctors → architects inside doctors
Statement 2: Some doctors are musicians → doctors and musicians overlap
Statement 3: No musicians is a scientists → musicians and scientists separate

Checking Conclusions:

✗ Conclusion I: "Some architects are not scientists"
Cannot determine relationship between architects and scientists - NOT PROVEN

✓ Conclusion II: "Some doctors are not scientists"
Some doctors are musicians (given) + No musicians is scientists (given)
Those doctors which are musicians cannot be scientists - FOLLOWS

✓ Conclusion III: "No scientists is a musicians"
Conversion of "No musicians is a scientists" - FOLLOWS

Answer: Conclusions II and III follow

Question 8

Statements: All principles are ideas. Some ideas are concepts. No concepts is a theories. Conclusions: I. Some principles are not theories. II. Some ideas are not theories. III. No theories is a concepts.

Step-by-Step Analysis:

Statement 1: All principles are ideas → principles inside ideas
Statement 2: Some ideas are concepts → ideas and concepts overlap
Statement 3: No concepts is a theories → concepts and theories separate

Checking Conclusions:

✗ Conclusion I: "Some principles are not theories"
Cannot determine relationship between principles and theories - NOT PROVEN

✓ Conclusion II: "Some ideas are not theories"
Some ideas are concepts (given) + No concepts is theories (given)
Those ideas which are concepts cannot be theories - FOLLOWS

✓ Conclusion III: "No theories is a concepts"
Conversion of "No concepts is a theories" - FOLLOWS

Answer: Conclusions II and III follow

Question 9

Statements: All durable are beautiful. Some beautiful are useful. No useful is a rare. Conclusions: I. Some durable are not rare. II. Some beautiful are not rare. III. No rare is a useful.

Step-by-Step Analysis:

Statement 1: All durable are beautiful → durable inside beautiful
Statement 2: Some beautiful are useful → beautiful and useful overlap
Statement 3: No useful is a rare → useful and rare separate

Checking Conclusions:

✗ Conclusion I: "Some durable are not rare"
Cannot determine relationship between durable and rare - NOT PROVEN

✓ Conclusion II: "Some beautiful are not rare"
Some beautiful are useful (given) + No useful is rare (given)
Those beautiful which are useful cannot be rare - FOLLOWS

✓ Conclusion III: "No rare is a useful"
Conversion of "No useful is a rare" - FOLLOWS

Answer: Conclusions II and III follow

Question 10

Statements: All models are ideas. Some ideas are patterns. No patterns is a frameworks. Conclusions: I. Some models are not frameworks. II. Some ideas are not frameworks. III. No frameworks is a patterns.

Step-by-Step Analysis:

Statement 1: All models are ideas → models inside ideas
Statement 2: Some ideas are patterns → ideas and patterns overlap
Statement 3: No patterns is a frameworks → patterns and frameworks separate

Checking Conclusions:

✗ Conclusion I: "Some models are not frameworks"
Cannot determine relationship between models and frameworks - NOT PROVEN

✓ Conclusion II: "Some ideas are not frameworks"
Some ideas are patterns (given) + No patterns is frameworks (given)
Those ideas which are patterns cannot be frameworks - FOLLOWS

✓ Conclusion III: "No frameworks is a patterns"
Conversion of "No patterns is a frameworks" - FOLLOWS

Answer: Conclusions II and III follow

Question 11

Statements: All accessible are durable. Some durable are valuable. No valuable is a sustainable. Conclusions: I. Some accessible are not sustainable. II. Some durable are not sustainable. III. No sustainable is a valuable.

Step-by-Step Analysis:

Statement 1: All accessible are durable → accessible inside durable
Statement 2: Some durable are valuable → durable and valuable overlap
Statement 3: No valuable is a sustainable → valuable and sustainable separate

Checking Conclusions:

✗ Conclusion I: "Some accessible are not sustainable"
Cannot determine relationship between accessible and sustainable - NOT PROVEN

✓ Conclusion II: "Some durable are not sustainable"
Some durable are valuable (given) + No valuable is sustainable (given)
Those durable which are valuable cannot be sustainable - FOLLOWS

✓ Conclusion III: "No sustainable is a valuable"
Conversion of "No valuable is a sustainable" - FOLLOWS

Answer: Conclusions II and III follow

Question 12

Statements: All useful are accessible. Some accessible are reliable. No reliable is a rare. Conclusions: I. Some useful are not rare. II. Some accessible are not rare. III. No rare is a reliable.

Step-by-Step Analysis:

Statement 1: All useful are accessible → useful inside accessible
Statement 2: Some accessible are reliable → accessible and reliable overlap
Statement 3: No reliable is a rare → reliable and rare separate

Checking Conclusions:

✗ Conclusion I: "Some useful are not rare"
Cannot determine relationship between useful and rare - NOT PROVEN

✓ Conclusion II: "Some accessible are not rare"
Some accessible are reliable (given) + No reliable is rare (given)
Those accessible which are reliable cannot be rare - FOLLOWS

✓ Conclusion III: "No rare is a reliable"
Conversion of "No reliable is a rare" - FOLLOWS

Answer: Conclusions II and III follow

Question 13

Statements: All diurnal are warm-blooded. Some warm-blooded are nocturnal. No nocturnal is a domestic. Conclusions: I. Some diurnal are not domestic. II. Some warm-blooded are not domestic. III. No domestic is a nocturnal.

Step-by-Step Analysis:

Statement 1: All diurnal are warm-blooded → diurnal inside warm-blooded
Statement 2: Some warm-blooded are nocturnal → warm-blooded and nocturnal overlap
Statement 3: No nocturnal is a domestic → nocturnal and domestic separate

Checking Conclusions:

✗ Conclusion I: "Some diurnal are not domestic"
Cannot determine relationship between diurnal and domestic - NOT PROVEN

✓ Conclusion II: "Some warm-blooded are not domestic"
Some warm-blooded are nocturnal (given) + No nocturnal is domestic (given)
Those warm-blooded which are nocturnal cannot be domestic - FOLLOWS

✓ Conclusion III: "No domestic is a nocturnal"
Conversion of "No nocturnal is a domestic" - FOLLOWS

Answer: Conclusions II and III follow

Question 14

Statements: All engineers are accountants. Some accountants are artists. No artists is a musicians. Conclusions: I. Some engineers are not musicians. II. Some accountants are not musicians. III. No musicians is a artists.

Step-by-Step Analysis:

Statement 1: All engineers are accountants → engineers inside accountants
Statement 2: Some accountants are artists → accountants and artists overlap
Statement 3: No artists is a musicians → artists and musicians separate

Checking Conclusions:

✗ Conclusion I: "Some engineers are not musicians"
Cannot determine relationship between engineers and musicians - NOT PROVEN

✓ Conclusion II: "Some accountants are not musicians"
Some accountants are artists (given) + No artists is musicians (given)
Those accountants which are artists cannot be musicians - FOLLOWS

✓ Conclusion III: "No musicians is a artists"
Conversion of "No artists is a musicians" - FOLLOWS

Answer: Conclusions II and III follow

Question 15

Statements: All domestic are carnivores. Some carnivores are invertebrates. No invertebrates is a wild. Conclusions: I. Some domestic are not wild. II. Some carnivores are not wild. III. No wild is a invertebrates.

Step-by-Step Analysis:

Statement 1: All domestic are carnivores → domestic inside carnivores
Statement 2: Some carnivores are invertebrates → carnivores and invertebrates overlap
Statement 3: No invertebrates is a wild → invertebrates and wild separate

Checking Conclusions:

✗ Conclusion I: "Some domestic are not wild"
Cannot determine relationship between domestic and wild - NOT PROVEN

✓ Conclusion II: "Some carnivores are not wild"
Some carnivores are invertebrates (given) + No invertebrates is wild (given)
Those carnivores which are invertebrates cannot be wild - FOLLOWS

✓ Conclusion III: "No wild is a invertebrates"
Conversion of "No invertebrates is a wild" - FOLLOWS

Answer: Conclusions II and III follow

Question 16

Statements: All nocturnal are invertebrates. Some invertebrates are warm-blooded. No warm-blooded is a fish. Conclusions: I. Some nocturnal are not fish. II. Some invertebrates are not fish. III. No fish is a warm-blooded.

Step-by-Step Analysis:

Statement 1: All nocturnal are invertebrates → nocturnal inside invertebrates
Statement 2: Some invertebrates are warm-blooded → invertebrates and warm-blooded overlap
Statement 3: No warm-blooded is a fish → warm-blooded and fish separate

Checking Conclusions:

✗ Conclusion I: "Some nocturnal are not fish"
Cannot determine relationship between nocturnal and fish - NOT PROVEN

✓ Conclusion II: "Some invertebrates are not fish"
Some invertebrates are warm-blooded (given) + No warm-blooded is fish (given)
Those invertebrates which are warm-blooded cannot be fish - FOLLOWS

✓ Conclusion III: "No fish is a warm-blooded"
Conversion of "No warm-blooded is a fish" - FOLLOWS

Answer: Conclusions II and III follow

Question 17

Statements: All methods are ideas. Some ideas are systems. No systems is a principles. Conclusions: I. Some methods are not principles. II. Some ideas are not principles. III. No principles is a systems.

Step-by-Step Analysis:

Statement 1: All methods are ideas → methods inside ideas
Statement 2: Some ideas are systems → ideas and systems overlap
Statement 3: No systems is a principles → systems and principles separate

Checking Conclusions:

✗ Conclusion I: "Some methods are not principles"
Cannot determine relationship between methods and principles - NOT PROVEN

✓ Conclusion II: "Some ideas are not principles"
Some ideas are systems (given) + No systems is principles (given)
Those ideas which are systems cannot be principles - FOLLOWS

✓ Conclusion III: "No principles is a systems"
Conversion of "No systems is a principles" - FOLLOWS

Answer: Conclusions II and III follow

Question 18

Statements: All engineers are teachers. Some teachers are athletes. No athletes is a pharmacists. Conclusions: I. Some engineers are not pharmacists. II. Some teachers are not pharmacists. III. No pharmacists is a athletes.

Step-by-Step Analysis:

Statement 1: All engineers are teachers → engineers inside teachers
Statement 2: Some teachers are athletes → teachers and athletes overlap
Statement 3: No athletes is a pharmacists → athletes and pharmacists separate

Checking Conclusions:

✗ Conclusion I: "Some engineers are not pharmacists"
Cannot determine relationship between engineers and pharmacists - NOT PROVEN

✓ Conclusion II: "Some teachers are not pharmacists"
Some teachers are athletes (given) + No athletes is pharmacists (given)
Those teachers which are athletes cannot be pharmacists - FOLLOWS

✓ Conclusion III: "No pharmacists is a athletes"
Conversion of "No athletes is a pharmacists" - FOLLOWS

Answer: Conclusions II and III follow

Question 19

Statements: All entrepreneurs are scientists. Some scientists are pharmacists. No pharmacists is a musicians. Conclusions: I. Some entrepreneurs are not musicians. II. Some scientists are not musicians. III. No musicians is a pharmacists.

Step-by-Step Analysis:

Statement 1: All entrepreneurs are scientists → entrepreneurs inside scientists
Statement 2: Some scientists are pharmacists → scientists and pharmacists overlap
Statement 3: No pharmacists is a musicians → pharmacists and musicians separate

Checking Conclusions:

✗ Conclusion I: "Some entrepreneurs are not musicians"
Cannot determine relationship between entrepreneurs and musicians - NOT PROVEN

✓ Conclusion II: "Some scientists are not musicians"
Some scientists are pharmacists (given) + No pharmacists is musicians (given)
Those scientists which are pharmacists cannot be musicians - FOLLOWS

✓ Conclusion III: "No musicians is a pharmacists"
Conversion of "No pharmacists is a musicians" - FOLLOWS

Answer: Conclusions II and III follow

Question 20

Statements: All tools are instruments. Some instruments are appliances. No appliances is a machines. Conclusions: I. Some tools are not machines. II. Some instruments are not machines. III. No machines is a appliances.

Step-by-Step Analysis:

Statement 1: All tools are instruments → tools inside instruments
Statement 2: Some instruments are appliances → instruments and appliances overlap
Statement 3: No appliances is a machines → appliances and machines separate

Checking Conclusions:

✗ Conclusion I: "Some tools are not machines"
Cannot determine relationship between tools and machines - NOT PROVEN

✓ Conclusion II: "Some instruments are not machines"
Some instruments are appliances (given) + No appliances is machines (given)
Those instruments which are appliances cannot be machines - FOLLOWS

✓ Conclusion III: "No machines is a appliances"
Conversion of "No appliances is a machines" - FOLLOWS

Answer: Conclusions II and III follow

Three Statement Standard: Worksheet 10 - Expert Practice Three Statement Standard EXPERT

What you'll learn in this worksheet: