Distribution of Terms | Worksheet 7/10 - Intermediate-Advanced self...

Question 1

Statements: All durable are innovative. Some durable are efficient. Conclusions: I. Some innovative are efficient. II. All innovative being efficient is a possibility. III. Some efficient are innovative.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All durable are innovative" → durable DISTRIBUTED, innovative UNDISTRIBUTED
Statement 2: "Some durable are efficient" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some innovative are efficient" - FOLLOWS
✓ Conclusion II: "All innovative being efficient is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some efficient are innovative" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 2

Statements: All nurses are doctors. Some nurses are athletes. Conclusions: I. Some doctors are athletes. II. All doctors being athletes is a possibility. III. Some athletes are doctors.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All nurses are doctors" → nurses DISTRIBUTED, doctors UNDISTRIBUTED
Statement 2: "Some nurses are athletes" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some doctors are athletes" - FOLLOWS
✓ Conclusion II: "All doctors being athletes is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some athletes are doctors" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 3

Statements: All accessible are essential. Some accessible are useful. Conclusions: I. Some essential are useful. II. All essential being useful is a possibility. III. Some useful are essential.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All accessible are essential" → accessible DISTRIBUTED, essential UNDISTRIBUTED
Statement 2: "Some accessible are useful" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some essential are useful" - FOLLOWS
✓ Conclusion II: "All essential being useful is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some useful are essential" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 4

Statements: All essential are reliable. Some essential are sustainable. Conclusions: I. Some reliable are sustainable. II. All reliable being sustainable is a possibility. III. Some sustainable are reliable.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All essential are reliable" → essential DISTRIBUTED, reliable UNDISTRIBUTED
Statement 2: "Some essential are sustainable" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some reliable are sustainable" - FOLLOWS
✓ Conclusion II: "All reliable being sustainable is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some sustainable are reliable" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 5

Statements: All theories are processes. Some theories are frameworks. Conclusions: I. Some processes are frameworks. II. All processes being frameworks is a possibility. III. Some frameworks are processes.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All theories are processes" → theories DISTRIBUTED, processes UNDISTRIBUTED
Statement 2: "Some theories are frameworks" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some processes are frameworks" - FOLLOWS
✓ Conclusion II: "All processes being frameworks is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some frameworks are processes" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 6

Statements: All carnivores are reptiles. Some carnivores are vertebrates. Conclusions: I. Some reptiles are vertebrates. II. All reptiles being vertebrates is a possibility. III. Some vertebrates are reptiles.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All carnivores are reptiles" → carnivores DISTRIBUTED, reptiles UNDISTRIBUTED
Statement 2: "Some carnivores are vertebrates" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some reptiles are vertebrates" - FOLLOWS
✓ Conclusion II: "All reptiles being vertebrates is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some vertebrates are reptiles" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 7

Statements: All useful are rare. Some useful are versatile. Conclusions: I. Some rare are versatile. II. All rare being versatile is a possibility. III. Some versatile are rare.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All useful are rare" → useful DISTRIBUTED, rare UNDISTRIBUTED
Statement 2: "Some useful are versatile" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some rare are versatile" - FOLLOWS
✓ Conclusion II: "All rare being versatile is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some versatile are rare" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 8

Statements: All frameworks are models. Some frameworks are concepts. Conclusions: I. Some models are concepts. II. All models being concepts is a possibility. III. Some concepts are models.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All frameworks are models" → frameworks DISTRIBUTED, models UNDISTRIBUTED
Statement 2: "Some frameworks are concepts" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some models are concepts" - FOLLOWS
✓ Conclusion II: "All models being concepts is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some concepts are models" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 9

Statements: All valuable are versatile. Some valuable are durable. Conclusions: I. Some versatile are durable. II. All versatile being durable is a possibility. III. Some durable are versatile.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All valuable are versatile" → valuable DISTRIBUTED, versatile UNDISTRIBUTED
Statement 2: "Some valuable are durable" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some versatile are durable" - FOLLOWS
✓ Conclusion II: "All versatile being durable is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some durable are versatile" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 10

Statements: All beautiful are innovative. Some beautiful are rare. Conclusions: I. Some innovative are rare. II. All innovative being rare is a possibility. III. Some rare are innovative.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All beautiful are innovative" → beautiful DISTRIBUTED, innovative UNDISTRIBUTED
Statement 2: "Some beautiful are rare" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some innovative are rare" - FOLLOWS
✓ Conclusion II: "All innovative being rare is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some rare are innovative" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 11

Statements: All invertebrates are nocturnal. Some invertebrates are omnivores. Conclusions: I. Some nocturnal are omnivores. II. All nocturnal being omnivores is a possibility. III. Some omnivores are nocturnal.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All invertebrates are nocturnal" → invertebrates DISTRIBUTED, nocturnal UNDISTRIBUTED
Statement 2: "Some invertebrates are omnivores" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some nocturnal are omnivores" - FOLLOWS
✓ Conclusion II: "All nocturnal being omnivores is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some omnivores are nocturnal" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 12

Statements: All frameworks are systems. Some frameworks are theories. Conclusions: I. Some systems are theories. II. All systems being theories is a possibility. III. Some theories are systems.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All frameworks are systems" → frameworks DISTRIBUTED, systems UNDISTRIBUTED
Statement 2: "Some frameworks are theories" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some systems are theories" - FOLLOWS
✓ Conclusion II: "All systems being theories is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some theories are systems" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 13

Statements: All equipment are tools. Some equipment are devices. Conclusions: I. Some tools are devices. II. All tools being devices is a possibility. III. Some devices are tools.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All equipment are tools" → equipment DISTRIBUTED, tools UNDISTRIBUTED
Statement 2: "Some equipment are devices" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some tools are devices" - FOLLOWS
✓ Conclusion II: "All tools being devices is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some devices are tools" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 14

Statements: All methods are structures. Some methods are systems. Conclusions: I. Some structures are systems. II. All structures being systems is a possibility. III. Some systems are structures.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All methods are structures" → methods DISTRIBUTED, structures UNDISTRIBUTED
Statement 2: "Some methods are systems" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some structures are systems" - FOLLOWS
✓ Conclusion II: "All structures being systems is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some systems are structures" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 15

Statements: All electronics are equipment. Some electronics are devices. Conclusions: I. Some equipment are devices. II. All equipment being devices is a possibility. III. Some devices are equipment.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All electronics are equipment" → electronics DISTRIBUTED, equipment UNDISTRIBUTED
Statement 2: "Some electronics are devices" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some equipment are devices" - FOLLOWS
✓ Conclusion II: "All equipment being devices is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some devices are equipment" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 16

Statements: All managers are lawyers. Some managers are scientists. Conclusions: I. Some lawyers are scientists. II. All lawyers being scientists is a possibility. III. Some scientists are lawyers.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All managers are lawyers" → managers DISTRIBUTED, lawyers UNDISTRIBUTED
Statement 2: "Some managers are scientists" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some lawyers are scientists" - FOLLOWS
✓ Conclusion II: "All lawyers being scientists is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some scientists are lawyers" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 17

Statements: All methods are frameworks. Some methods are theories. Conclusions: I. Some frameworks are theories. II. All frameworks being theories is a possibility. III. Some theories are frameworks.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All methods are frameworks" → methods DISTRIBUTED, frameworks UNDISTRIBUTED
Statement 2: "Some methods are theories" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some frameworks are theories" - FOLLOWS
✓ Conclusion II: "All frameworks being theories is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some theories are frameworks" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 18

Statements: All beautiful are efficient. Some beautiful are rare. Conclusions: I. Some efficient are rare. II. All efficient being rare is a possibility. III. Some rare are efficient.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All beautiful are efficient" → beautiful DISTRIBUTED, efficient UNDISTRIBUTED
Statement 2: "Some beautiful are rare" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some efficient are rare" - FOLLOWS
✓ Conclusion II: "All efficient being rare is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some rare are efficient" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 19

Statements: All structures are processes. Some structures are frameworks. Conclusions: I. Some processes are frameworks. II. All processes being frameworks is a possibility. III. Some frameworks are processes.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All structures are processes" → structures DISTRIBUTED, processes UNDISTRIBUTED
Statement 2: "Some structures are frameworks" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some processes are frameworks" - FOLLOWS
✓ Conclusion II: "All processes being frameworks is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some frameworks are processes" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 20

Statements: All efficient are rare. Some efficient are accessible. Conclusions: I. Some rare are accessible. II. All rare being accessible is a possibility. III. Some accessible are rare.

Distribution of Terms:
A term is DISTRIBUTED when statement makes claim about ALL members.
A term is UNDISTRIBUTED when statement refers to SOME members.

Statement Analysis:
Statement 1: "All efficient are rare" → efficient DISTRIBUTED, rare UNDISTRIBUTED
Statement 2: "Some efficient are accessible" → Both UNDISTRIBUTED

Logical Deduction:
Some B are C (I) + All B are A (A) = I + A = I
Result: Some C are A OR Some A are C

Checking Conclusions:
✓ Conclusion I: "Some rare are accessible" - FOLLOWS
✓ Conclusion II: "All rare being accessible is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some accessible are rare" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

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