Distribution of Terms | Worksheet 6/10 - Intermediate-Advanced time...

Question 1

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

Answer: All conclusions I, II and III follow

Question 2

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

Answer: All conclusions I, II and III follow

Question 3

Statements: All utensils are vehicles. Some utensils are furniture. Conclusions: I. Some vehicles are furniture. II. All vehicles being furniture is a possibility. III. Some furniture are vehicles.

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

Answer: All conclusions I, II and III follow

Question 4

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

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

Answer: All conclusions I, II and III follow

Question 5

Statements: All omnivores are fish. Some omnivores are herbivores. Conclusions: I. Some fish are herbivores. II. All fish being herbivores is a possibility. III. Some herbivores are fish.

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

Answer: All conclusions I, II and III follow

Question 6

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

Answer: All conclusions I, II and III follow

Question 7

Statements: All lawyers are architects. Some lawyers are pharmacists. Conclusions: I. Some architects are pharmacists. II. All architects being pharmacists is a possibility. III. Some pharmacists are architects.

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

Answer: All conclusions I, II and III follow

Question 8

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

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

Answer: All conclusions I, II and III follow

Question 9

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

Answer: All conclusions I, II and III follow

Question 10

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

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

Answer: All conclusions I, II and III follow

Question 11

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

Answer: All conclusions I, II and III follow

Question 12

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

Answer: All conclusions I, II and III follow

Question 13

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

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

Answer: All conclusions I, II and III follow

Question 14

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

Answer: All conclusions I, II and III follow

Question 15

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

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

Answer: All conclusions I, II and III follow

Question 16

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

Answer: All conclusions I, II and III follow

Question 17

Statements: All carnivores are wild. Some carnivores are vertebrates. Conclusions: I. Some wild are vertebrates. II. All wild being vertebrates is a possibility. III. Some vertebrates 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 carnivores are wild" → carnivores DISTRIBUTED, wild 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 wild are vertebrates" - FOLLOWS
✓ Conclusion II: "All wild being vertebrates is a possibility" - No negatives exist - FOLLOWS
✓ Conclusion III: "Some vertebrates are wild" - Conversion of I - FOLLOWS

Answer: All conclusions I, II and III follow

Question 18

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

Answer: All conclusions I, II and III follow

Question 19

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

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

Answer: All conclusions I, II and III follow

Question 20

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

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

Answer: All conclusions I, II and III follow

Distribution of Terms: Worksheet 6 - Intermediate-Advanced Practice Distribution of Terms INTERMEDIATE ADVANCED

What you'll learn in this worksheet: