Distribution of Terms | Worksheet 8/10 - Advanced exam hall simulat...

Question 1

Statements: All electronics are appliances. Some electronics are vehicles. Conclusions: I. Some appliances are vehicles. II. All appliances being vehicles is a possibility. III. Some vehicles are appliances.

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 appliances" → electronics DISTRIBUTED, appliances UNDISTRIBUTED
Statement 2: "Some electronics are vehicles" → 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 appliances are vehicles" - FOLLOWS
✓ Conclusion II: "All appliances being vehicles is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some vehicles are appliances" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 2

Statements: All herbivores are nocturnal. Some herbivores are mammals. Conclusions: I. Some nocturnal are mammals. II. All nocturnal being mammals is a possibility. III. Some mammals 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 herbivores are nocturnal" → herbivores DISTRIBUTED, nocturnal UNDISTRIBUTED
Statement 2: "Some herbivores are mammals" → 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 mammals" - FOLLOWS
✓ Conclusion II: "All nocturnal being mammals is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some mammals are nocturnal" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 3

Statements: All diurnal are amphibians. Some diurnal are wild. Conclusions: I. Some amphibians are wild. II. All amphibians being wild is a possibility. III. Some wild are amphibians.

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 diurnal are amphibians" → diurnal DISTRIBUTED, amphibians UNDISTRIBUTED
Statement 2: "Some diurnal are wild" → 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 amphibians are wild" - FOLLOWS
✓ Conclusion II: "All amphibians being wild is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some wild are amphibians" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 4

Statements: All managers are entrepreneurs. Some managers are athletes. Conclusions: I. Some entrepreneurs are athletes. II. All entrepreneurs being athletes is a possibility. III. Some athletes are entrepreneurs.

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 entrepreneurs" → managers DISTRIBUTED, entrepreneurs UNDISTRIBUTED
Statement 2: "Some managers 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 entrepreneurs are athletes" - FOLLOWS
✓ Conclusion II: "All entrepreneurs being athletes is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some athletes are entrepreneurs" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 5

Statements: All devices are machines. Some devices are furniture. Conclusions: I. Some machines are furniture. II. All machines being furniture is a possibility. III. Some furniture are machines.

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 devices are machines" → devices DISTRIBUTED, machines UNDISTRIBUTED
Statement 2: "Some devices are furniture" → 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 machines are furniture" - FOLLOWS
✓ Conclusion II: "All machines being furniture is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some furniture are machines" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 6

Statements: All machines are instruments. Some machines are appliances. Conclusions: I. Some instruments are appliances. II. All instruments being appliances is a possibility. III. Some appliances are instruments.

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 machines are instruments" → machines DISTRIBUTED, instruments UNDISTRIBUTED
Statement 2: "Some machines are appliances" → 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 instruments are appliances" - FOLLOWS
✓ Conclusion II: "All instruments being appliances is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some appliances are instruments" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 7

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

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 beautiful" → useful DISTRIBUTED, beautiful UNDISTRIBUTED
Statement 2: "Some useful 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 beautiful are accessible" - FOLLOWS
✓ Conclusion II: "All beautiful being accessible is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some accessible are beautiful" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 8

Statements: All furniture are instruments. Some furniture are devices. Conclusions: I. Some instruments are devices. II. All instruments being devices is a possibility. III. Some devices are instruments.

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 furniture are instruments" → furniture DISTRIBUTED, instruments UNDISTRIBUTED
Statement 2: "Some furniture 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 instruments are devices" - FOLLOWS
✓ Conclusion II: "All instruments being devices is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some devices are instruments" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 9

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

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 teachers are nurses" → teachers DISTRIBUTED, nurses UNDISTRIBUTED
Statement 2: "Some teachers are doctors" → 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 nurses are doctors" - FOLLOWS
✓ Conclusion II: "All nurses being doctors is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some doctors are nurses" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 10

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

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 reliable are sustainable" → reliable DISTRIBUTED, sustainable UNDISTRIBUTED
Statement 2: "Some reliable 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 sustainable are accessible" - FOLLOWS
✓ Conclusion II: "All sustainable being accessible is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some accessible are sustainable" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 11

Statements: All models are systems. Some models are frameworks. Conclusions: I. Some systems are frameworks. II. All systems being frameworks is a possibility. III. Some frameworks 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 models are systems" → models DISTRIBUTED, systems UNDISTRIBUTED
Statement 2: "Some models 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 systems are frameworks" - FOLLOWS
✓ Conclusion II: "All systems being frameworks is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some frameworks are systems" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 12

Statements: All pilots are scientists. Some pilots are athletes. Conclusions: I. Some scientists are athletes. II. All scientists being athletes is a possibility. III. Some athletes are scientists.

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 pilots are scientists" → pilots DISTRIBUTED, scientists UNDISTRIBUTED
Statement 2: "Some pilots 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 scientists are athletes" - FOLLOWS
✓ Conclusion II: "All scientists being athletes is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some athletes are scientists" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 13

Statements: All rare are essential. Some rare are versatile. Conclusions: I. Some essential are versatile. II. All essential being versatile is a possibility. III. Some versatile 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 rare are essential" → rare DISTRIBUTED, essential UNDISTRIBUTED
Statement 2: "Some rare 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 essential are versatile" - FOLLOWS
✓ Conclusion II: "All essential being versatile is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some versatile are essential" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 14

Statements: All nurses are engineers. Some nurses are pilots. Conclusions: I. Some engineers are pilots. II. All engineers being pilots is a possibility. III. Some pilots are engineers.

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 engineers" → nurses DISTRIBUTED, engineers UNDISTRIBUTED
Statement 2: "Some nurses are pilots" → 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 engineers are pilots" - FOLLOWS
✓ Conclusion II: "All engineers being pilots is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some pilots are engineers" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 15

Statements: All birds are amphibians. Some birds are invertebrates. Conclusions: I. Some amphibians are invertebrates. II. All amphibians being invertebrates is a possibility. III. Some invertebrates are amphibians.

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 birds are amphibians" → birds DISTRIBUTED, amphibians UNDISTRIBUTED
Statement 2: "Some birds are invertebrates" → 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 amphibians are invertebrates" - FOLLOWS
✓ Conclusion II: "All amphibians being invertebrates is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some invertebrates are amphibians" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 16

Statements: All warm-blooded are diurnal. Some warm-blooded are invertebrates. Conclusions: I. Some diurnal are invertebrates. II. All diurnal being invertebrates is a possibility. III. Some invertebrates are diurnal.

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 warm-blooded are diurnal" → warm-blooded DISTRIBUTED, diurnal UNDISTRIBUTED
Statement 2: "Some warm-blooded are invertebrates" → 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 diurnal are invertebrates" - FOLLOWS
✓ Conclusion II: "All diurnal being invertebrates is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some invertebrates are diurnal" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 17

Statements: All musicians are scientists. Some musicians are writers. Conclusions: I. Some scientists are writers. II. All scientists being writers is a possibility. III. Some writers are scientists.

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 musicians are scientists" → musicians DISTRIBUTED, scientists UNDISTRIBUTED
Statement 2: "Some musicians are writers" → 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 scientists are writers" - FOLLOWS
✓ Conclusion II: "All scientists being writers is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some writers are scientists" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 18

Statements: All theories are patterns. Some theories are ideas. Conclusions: I. Some patterns are ideas. II. All patterns being ideas is a possibility. III. Some ideas are patterns.

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 patterns" → theories DISTRIBUTED, patterns UNDISTRIBUTED
Statement 2: "Some theories are ideas" → 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 patterns are ideas" - FOLLOWS
✓ Conclusion II: "All patterns being ideas is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some ideas are patterns" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 19

Statements: All birds are domestic. Some birds are nocturnal. Conclusions: I. Some domestic are nocturnal. II. All domestic being nocturnal is a possibility. III. Some nocturnal are domestic.

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 birds are domestic" → birds DISTRIBUTED, domestic UNDISTRIBUTED
Statement 2: "Some birds are nocturnal" → 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 domestic are nocturnal" - FOLLOWS
✓ Conclusion II: "All domestic being nocturnal is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some nocturnal are domestic" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 20

Statements: All engineers are musicians. Some engineers are lawyers. Conclusions: I. Some musicians are lawyers. II. All musicians being lawyers is a possibility. III. Some lawyers are musicians.

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 engineers are musicians" → engineers DISTRIBUTED, musicians UNDISTRIBUTED
Statement 2: "Some engineers are lawyers" → 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 musicians are lawyers" - FOLLOWS
✓ Conclusion II: "All musicians being lawyers is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some lawyers are musicians" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Distribution of Terms Advanced Worksheet: Focus on exam-oriented approach Distribution of Terms ADVANCED

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