Distribution of Terms | Worksheet 3/10 - Beginner skill builder ⚡ |...

Question 1

Statements: All mammals are wild. Some mammals are nocturnal. Conclusions: I. Some wild are nocturnal. II. All wild being nocturnal is a possibility. III. Some nocturnal are wild.

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

Answer: All conclusions I, II and III follow

Question 2

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

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

Answer: All conclusions I, II and III follow

Question 3

Statements: All writers are accountants. Some writers are nurses. Conclusions: I. Some accountants are nurses. II. All accountants being nurses is a possibility. III. Some nurses are accountants.

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

Answer: All conclusions I, II and III follow

Question 4

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

Answer: All conclusions I, II and III follow

Question 5

Statements: All architects are managers. Some architects are musicians. Conclusions: I. Some managers are musicians. II. All managers being musicians is a possibility. III. Some musicians are managers.

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

Answer: All conclusions I, II and III follow

Question 6

Statements: All fish are wild. Some fish are carnivores. Conclusions: I. Some wild are carnivores. II. All wild being carnivores is a possibility. III. Some carnivores are wild.

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

Answer: All conclusions I, II and III follow

Question 7

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

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

Answer: All conclusions I, II and III follow

Question 8

Statements: All structures are ideas. Some structures are strategies. Conclusions: I. Some ideas are strategies. II. All ideas being strategies is a possibility. III. Some strategies are ideas.

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

Answer: All conclusions I, II and III follow

Question 9

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

Answer: All conclusions I, II and III follow

Question 10

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

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

Answer: All conclusions I, II and III follow

Question 11

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

Answer: All conclusions I, II and III follow

Question 12

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

Answer: All conclusions I, II and III follow

Question 13

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

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

Answer: All conclusions I, II and III follow

Question 14

Statements: All nurses are engineers. Some nurses are teachers. Conclusions: I. Some engineers are teachers. II. All engineers being teachers is a possibility. III. Some teachers 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 teachers" → 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 teachers" - FOLLOWS
✓ Conclusion II: "All engineers being teachers is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some teachers are engineers" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 15

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

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

Answer: All conclusions I, II and III follow

Question 16

Statements: All appliances are furniture. Some appliances are equipment. Conclusions: I. Some furniture are equipment. II. All furniture being equipment is a possibility. III. Some equipment are furniture.

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

Answer: All conclusions I, II and III follow

Question 17

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

Answer: All conclusions I, II and III follow

Question 18

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

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

Answer: All conclusions I, II and III follow

Question 19

Statements: All pilots are teachers. Some pilots are architects. Conclusions: I. Some teachers are architects. II. All teachers being architects is a possibility. III. Some architects are teachers.

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

Answer: All conclusions I, II and III follow

Question 20

Statements: All fish are mammals. Some fish are nocturnal. Conclusions: I. Some mammals are nocturnal. II. All mammals being nocturnal is a possibility. III. Some nocturnal are mammals.

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

Answer: All conclusions I, II and III follow

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