Basic All-All Syllogism: Worksheet 10 - Expert Practice Basic All-All Syllogism EXPERT

Venn Diagram Method:
Draw three circles for fish, carnivores, and mammals.

Step 1: "All fish are carnivores" → Circle of fish completely inside carnivores
Step 2: "All carnivores are mammals" → Circle of carnivores completely inside mammals
Step 3: Result: fish ⊂ carnivores ⊂ mammals

Analytical Method (A + A = A):
All fish are carnivores (A) + All carnivores are mammals (A) = All fish are mammals (A)

Verification:
✓ Conclusion I: "All fish are mammals" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some mammals are fish" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for sustainable, beautiful, and reliable.

Step 1: "All sustainable are beautiful" → Circle of sustainable completely inside beautiful
Step 2: "All beautiful are reliable" → Circle of beautiful completely inside reliable
Step 3: Result: sustainable ⊂ beautiful ⊂ reliable

Analytical Method (A + A = A):
All sustainable are beautiful (A) + All beautiful are reliable (A) = All sustainable are reliable (A)

Verification:
✓ Conclusion I: "All sustainable are reliable" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some reliable are sustainable" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for utensils, electronics, and vehicles.

Step 1: "All utensils are electronics" → Circle of utensils completely inside electronics
Step 2: "All electronics are vehicles" → Circle of electronics completely inside vehicles
Step 3: Result: utensils ⊂ electronics ⊂ vehicles

Analytical Method (A + A = A):
All utensils are electronics (A) + All electronics are vehicles (A) = All utensils are vehicles (A)

Verification:
✓ Conclusion I: "All utensils are vehicles" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some vehicles are utensils" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for managers, artists, and accountants.

Step 1: "All managers are artists" → Circle of managers completely inside artists
Step 2: "All artists are accountants" → Circle of artists completely inside accountants
Step 3: Result: managers ⊂ artists ⊂ accountants

Analytical Method (A + A = A):
All managers are artists (A) + All artists are accountants (A) = All managers are accountants (A)

Verification:
✓ Conclusion I: "All managers are accountants" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some accountants are managers" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for models, structures, and strategies.

Step 1: "All models are structures" → Circle of models completely inside structures
Step 2: "All structures are strategies" → Circle of structures completely inside strategies
Step 3: Result: models ⊂ structures ⊂ strategies

Analytical Method (A + A = A):
All models are structures (A) + All structures are strategies (A) = All models are strategies (A)

Verification:
✓ Conclusion I: "All models are strategies" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some strategies are models" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for efficient, useful, and versatile.

Step 1: "All efficient are useful" → Circle of efficient completely inside useful
Step 2: "All useful are versatile" → Circle of useful completely inside versatile
Step 3: Result: efficient ⊂ useful ⊂ versatile

Analytical Method (A + A = A):
All efficient are useful (A) + All useful are versatile (A) = All efficient are versatile (A)

Verification:
✓ Conclusion I: "All efficient are versatile" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some versatile are efficient" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for processes, concepts, and ideas.

Step 1: "All processes are concepts" → Circle of processes completely inside concepts
Step 2: "All concepts are ideas" → Circle of concepts completely inside ideas
Step 3: Result: processes ⊂ concepts ⊂ ideas

Analytical Method (A + A = A):
All processes are concepts (A) + All concepts are ideas (A) = All processes are ideas (A)

Verification:
✓ Conclusion I: "All processes are ideas" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some ideas are processes" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for electronics, tools, and machines.

Step 1: "All electronics are tools" → Circle of electronics completely inside tools
Step 2: "All tools are machines" → Circle of tools completely inside machines
Step 3: Result: electronics ⊂ tools ⊂ machines

Analytical Method (A + A = A):
All electronics are tools (A) + All tools are machines (A) = All electronics are machines (A)

Verification:
✓ Conclusion I: "All electronics are machines" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some machines are electronics" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for herbivores, mammals, and invertebrates.

Step 1: "All herbivores are mammals" → Circle of herbivores completely inside mammals
Step 2: "All mammals are invertebrates" → Circle of mammals completely inside invertebrates
Step 3: Result: herbivores ⊂ mammals ⊂ invertebrates

Analytical Method (A + A = A):
All herbivores are mammals (A) + All mammals are invertebrates (A) = All herbivores are invertebrates (A)

Verification:
✓ Conclusion I: "All herbivores are invertebrates" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some invertebrates are herbivores" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for accessible, reliable, and versatile.

Step 1: "All accessible are reliable" → Circle of accessible completely inside reliable
Step 2: "All reliable are versatile" → Circle of reliable completely inside versatile
Step 3: Result: accessible ⊂ reliable ⊂ versatile

Analytical Method (A + A = A):
All accessible are reliable (A) + All reliable are versatile (A) = All accessible are versatile (A)

Verification:
✓ Conclusion I: "All accessible are versatile" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some versatile are accessible" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for principles, structures, and ideas.

Step 1: "All principles are structures" → Circle of principles completely inside structures
Step 2: "All structures are ideas" → Circle of structures completely inside ideas
Step 3: Result: principles ⊂ structures ⊂ ideas

Analytical Method (A + A = A):
All principles are structures (A) + All structures are ideas (A) = All principles are ideas (A)

Verification:
✓ Conclusion I: "All principles are ideas" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some ideas are principles" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for frameworks, models, and concepts.

Step 1: "All frameworks are models" → Circle of frameworks completely inside models
Step 2: "All models are concepts" → Circle of models completely inside concepts
Step 3: Result: frameworks ⊂ models ⊂ concepts

Analytical Method (A + A = A):
All frameworks are models (A) + All models are concepts (A) = All frameworks are concepts (A)

Verification:
✓ Conclusion I: "All frameworks are concepts" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some concepts are frameworks" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for rare, reliable, and essential.

Step 1: "All rare are reliable" → Circle of rare completely inside reliable
Step 2: "All reliable are essential" → Circle of reliable completely inside essential
Step 3: Result: rare ⊂ reliable ⊂ essential

Analytical Method (A + A = A):
All rare are reliable (A) + All reliable are essential (A) = All rare are essential (A)

Verification:
✓ Conclusion I: "All rare are essential" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some essential are rare" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for instruments, electronics, and furniture.

Step 1: "All instruments are electronics" → Circle of instruments completely inside electronics
Step 2: "All electronics are furniture" → Circle of electronics completely inside furniture
Step 3: Result: instruments ⊂ electronics ⊂ furniture

Analytical Method (A + A = A):
All instruments are electronics (A) + All electronics are furniture (A) = All instruments are furniture (A)

Verification:
✓ Conclusion I: "All instruments are furniture" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some furniture are instruments" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for equipment, tools, and ornaments.

Step 1: "All equipment are tools" → Circle of equipment completely inside tools
Step 2: "All tools are ornaments" → Circle of tools completely inside ornaments
Step 3: Result: equipment ⊂ tools ⊂ ornaments

Analytical Method (A + A = A):
All equipment are tools (A) + All tools are ornaments (A) = All equipment are ornaments (A)

Verification:
✓ Conclusion I: "All equipment are ornaments" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some ornaments are equipment" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for engineers, writers, and architects.

Step 1: "All engineers are writers" → Circle of engineers completely inside writers
Step 2: "All writers are architects" → Circle of writers completely inside architects
Step 3: Result: engineers ⊂ writers ⊂ architects

Analytical Method (A + A = A):
All engineers are writers (A) + All writers are architects (A) = All engineers are architects (A)

Verification:
✓ Conclusion I: "All engineers are architects" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some architects are engineers" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for vehicles, electronics, and devices.

Step 1: "All vehicles are electronics" → Circle of vehicles completely inside electronics
Step 2: "All electronics are devices" → Circle of electronics completely inside devices
Step 3: Result: vehicles ⊂ electronics ⊂ devices

Analytical Method (A + A = A):
All vehicles are electronics (A) + All electronics are devices (A) = All vehicles are devices (A)

Verification:
✓ Conclusion I: "All vehicles are devices" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some devices are vehicles" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for engineers, pharmacists, and teachers.

Step 1: "All engineers are pharmacists" → Circle of engineers completely inside pharmacists
Step 2: "All pharmacists are teachers" → Circle of pharmacists completely inside teachers
Step 3: Result: engineers ⊂ pharmacists ⊂ teachers

Analytical Method (A + A = A):
All engineers are pharmacists (A) + All pharmacists are teachers (A) = All engineers are teachers (A)

Verification:
✓ Conclusion I: "All engineers are teachers" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some teachers are engineers" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for utensils, ornaments, and machines.

Step 1: "All utensils are ornaments" → Circle of utensils completely inside ornaments
Step 2: "All ornaments are machines" → Circle of ornaments completely inside machines
Step 3: Result: utensils ⊂ ornaments ⊂ machines

Analytical Method (A + A = A):
All utensils are ornaments (A) + All ornaments are machines (A) = All utensils are machines (A)

Verification:
✓ Conclusion I: "All utensils are machines" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some machines are utensils" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow

Venn Diagram Method:
Draw three circles for mammals, nocturnal, and herbivores.

Step 1: "All mammals are nocturnal" → Circle of mammals completely inside nocturnal
Step 2: "All nocturnal are herbivores" → Circle of nocturnal completely inside herbivores
Step 3: Result: mammals ⊂ nocturnal ⊂ herbivores

Analytical Method (A + A = A):
All mammals are nocturnal (A) + All nocturnal are herbivores (A) = All mammals are herbivores (A)

Verification:
✓ Conclusion I: "All mammals are herbivores" - FOLLOWS (direct rule application)
✓ Conclusion II: "Some herbivores are mammals" - FOLLOWS (if all A are C, then some C are A)

Answer: Both conclusions I and II follow