Distribution of Terms | Worksheet 2/10 - Beginner entry level pract...

Question 1

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

Answer: All conclusions I, II and III follow

Question 2

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

Answer: All conclusions I, II and III follow

Question 3

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

Answer: All conclusions I, II and III follow

Question 4

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

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

Answer: All conclusions I, II and III follow

Question 5

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

Answer: All conclusions I, II and III follow

Question 6

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

Answer: All conclusions I, II and III follow

Question 7

Statements: All teachers are artists. Some teachers are athletes. Conclusions: I. Some artists are athletes. II. All artists being athletes is a possibility. III. Some athletes are artists.

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

Answer: All conclusions I, II and III follow

Question 8

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

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

Answer: All conclusions I, II and III follow

Question 9

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

Answer: All conclusions I, II and III follow

Question 10

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

Answer: All conclusions I, II and III follow

Question 11

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

Answer: All conclusions I, II and III follow

Question 12

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

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

Answer: All conclusions I, II and III follow

Question 13

Statements: All reliable are beautiful. Some reliable 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 reliable are beautiful" → reliable DISTRIBUTED, beautiful 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 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 14

Statements: All wild are mammals. Some wild 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 wild are mammals" → wild DISTRIBUTED, mammals UNDISTRIBUTED
Statement 2: "Some wild 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 15

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

Answer: All conclusions I, II and III follow

Question 16

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

Answer: All conclusions I, II and III follow

Question 17

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

Answer: All conclusions I, II and III follow

Question 18

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

Answer: All conclusions I, II and III follow

Question 19

Statements: All rare are valuable. Some rare are essential. Conclusions: I. Some valuable are essential. II. All valuable being essential is a possibility. III. Some essential are valuable.

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

Answer: All conclusions I, II and III follow

Question 20

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

Answer: All conclusions I, II and III follow

Distribution of Terms: Worksheet 2 - Beginner Practice Distribution of Terms BEGINNER

What you'll learn in this worksheet: