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Basic All-All Syllogism: Worksheet 6 - Intermediate-Advanced Practice Basic All-All Syllogism INTERMEDIATE ADVANCED

Ready to master Basic All-All Syllogism? This timed practice ⚡ worksheet (6/10) presents 20 intermediate-advanced-level challenges. Focus area: distribution of terms in 'all' statements. Learn to solve basic all-all syllogism tricks, handle basic all-all syllogism shortcut methods, and perfect basic all-all syllogism bank exam questions with our step-by-step solutions.

📝 Worksheet 6 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate Advanced level

What you'll learn in this worksheet:
Your progress through Basic All-All Syllogism
Worksheet 6 of 10 (55% complete)

Question 1

Statements: All instruments are ornaments. All ornaments are appliances. Conclusions: I. All instruments are appliances. II. Some appliances are instruments.
Venn Diagram Method:
Draw three circles for instruments, ornaments, and appliances.

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

Analytical Method (A + A = A):
All instruments are ornaments (A) + All ornaments are appliances (A) = All instruments are appliances (A)

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

Answer: Both conclusions I and II follow

Question 2

Statements: All nocturnal are cold-blooded. All cold-blooded are herbivores. Conclusions: I. All nocturnal are herbivores. II. Some herbivores are nocturnal.
Venn Diagram Method:
Draw three circles for nocturnal, cold-blooded, and herbivores.

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

Analytical Method (A + A = A):
All nocturnal are cold-blooded (A) + All cold-blooded are herbivores (A) = All nocturnal are herbivores (A)

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

Answer: Both conclusions I and II follow

Question 3

Statements: All teachers are lawyers. All lawyers are nurses. Conclusions: I. All teachers are nurses. II. Some nurses are teachers.
Venn Diagram Method:
Draw three circles for teachers, lawyers, and nurses.

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

Analytical Method (A + A = A):
All teachers are lawyers (A) + All lawyers are nurses (A) = All teachers are nurses (A)

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

Answer: Both conclusions I and II follow

Question 4

Statements: All artists are engineers. All engineers are doctors. Conclusions: I. All artists are doctors. II. Some doctors are artists.
Venn Diagram Method:
Draw three circles for artists, engineers, and doctors.

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

Analytical Method (A + A = A):
All artists are engineers (A) + All engineers are doctors (A) = All artists are doctors (A)

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

Answer: Both conclusions I and II follow

Question 5

Statements: All theories are processes. All processes are patterns. Conclusions: I. All theories are patterns. II. Some patterns are theories.
Venn Diagram Method:
Draw three circles for theories, processes, and patterns.

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

Analytical Method (A + A = A):
All theories are processes (A) + All processes are patterns (A) = All theories are patterns (A)

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

Answer: Both conclusions I and II follow

Question 6

Statements: All scientists are teachers. All teachers are architects. Conclusions: I. All scientists are architects. II. Some architects are scientists.
Venn Diagram Method:
Draw three circles for scientists, teachers, and architects.

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

Analytical Method (A + A = A):
All scientists are teachers (A) + All teachers are architects (A) = All scientists are architects (A)

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

Answer: Both conclusions I and II follow

Question 7

Statements: All versatile are durable. All durable are sustainable. Conclusions: I. All versatile are sustainable. II. Some sustainable are versatile.
Venn Diagram Method:
Draw three circles for versatile, durable, and sustainable.

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

Analytical Method (A + A = A):
All versatile are durable (A) + All durable are sustainable (A) = All versatile are sustainable (A)

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

Answer: Both conclusions I and II follow

Question 8

Statements: All devices are machines. All machines are tools. Conclusions: I. All devices are tools. II. Some tools are devices.
Venn Diagram Method:
Draw three circles for devices, machines, and tools.

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

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

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

Answer: Both conclusions I and II follow

Question 9

Statements: All patterns are strategies. All strategies are principles. Conclusions: I. All patterns are principles. II. Some principles are patterns.
Venn Diagram Method:
Draw three circles for patterns, strategies, and principles.

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

Analytical Method (A + A = A):
All patterns are strategies (A) + All strategies are principles (A) = All patterns are principles (A)

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

Answer: Both conclusions I and II follow

Question 10

Statements: All versatile are reliable. All reliable are useful. Conclusions: I. All versatile are useful. II. Some useful are versatile.
Venn Diagram Method:
Draw three circles for versatile, reliable, and useful.

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

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

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

Answer: Both conclusions I and II follow

Question 11

Statements: All systems are patterns. All patterns are models. Conclusions: I. All systems are models. II. Some models are systems.
Venn Diagram Method:
Draw three circles for systems, patterns, and models.

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

Analytical Method (A + A = A):
All systems are patterns (A) + All patterns are models (A) = All systems are models (A)

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

Answer: Both conclusions I and II follow

Question 12

Statements: All tools are vehicles. All vehicles are gadgets. Conclusions: I. All tools are gadgets. II. Some gadgets are tools.
Venn Diagram Method:
Draw three circles for tools, vehicles, and gadgets.

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

Analytical Method (A + A = A):
All tools are vehicles (A) + All vehicles are gadgets (A) = All tools are gadgets (A)

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

Answer: Both conclusions I and II follow

Question 13

Statements: All architects are pilots. All pilots are teachers. Conclusions: I. All architects are teachers. II. Some teachers are architects.
Venn Diagram Method:
Draw three circles for architects, pilots, and teachers.

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

Analytical Method (A + A = A):
All architects are pilots (A) + All pilots are teachers (A) = All architects are teachers (A)

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

Answer: Both conclusions I and II follow

Question 14

Statements: All nocturnal are cold-blooded. All cold-blooded are fish. Conclusions: I. All nocturnal are fish. II. Some fish are nocturnal.
Venn Diagram Method:
Draw three circles for nocturnal, cold-blooded, and fish.

Step 1: "All nocturnal are cold-blooded" → Circle of nocturnal completely inside cold-blooded
Step 2: "All cold-blooded are fish" → Circle of cold-blooded completely inside fish
Step 3: Result: nocturnal ⊂ cold-blooded ⊂ fish

Analytical Method (A + A = A):
All nocturnal are cold-blooded (A) + All cold-blooded are fish (A) = All nocturnal are fish (A)

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

Answer: Both conclusions I and II follow

Question 15

Statements: All accountants are doctors. All doctors are pharmacists. Conclusions: I. All accountants are pharmacists. II. Some pharmacists are accountants.
Venn Diagram Method:
Draw three circles for accountants, doctors, and pharmacists.

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

Analytical Method (A + A = A):
All accountants are doctors (A) + All doctors are pharmacists (A) = All accountants are pharmacists (A)

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

Answer: Both conclusions I and II follow

Question 16

Statements: All pharmacists are architects. All architects are athletes. Conclusions: I. All pharmacists are athletes. II. Some athletes are pharmacists.
Venn Diagram Method:
Draw three circles for pharmacists, architects, and athletes.

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

Analytical Method (A + A = A):
All pharmacists are architects (A) + All architects are athletes (A) = All pharmacists are athletes (A)

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

Answer: Both conclusions I and II follow

Question 17

Statements: All ornaments are electronics. All electronics are equipment. Conclusions: I. All ornaments are equipment. II. Some equipment are ornaments.
Venn Diagram Method:
Draw three circles for ornaments, electronics, and equipment.

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

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

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

Answer: Both conclusions I and II follow

Question 18

Statements: All innovative are accessible. All accessible are efficient. Conclusions: I. All innovative are efficient. II. Some efficient are innovative.
Venn Diagram Method:
Draw three circles for innovative, accessible, and efficient.

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

Analytical Method (A + A = A):
All innovative are accessible (A) + All accessible are efficient (A) = All innovative are efficient (A)

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

Answer: Both conclusions I and II follow

Question 19

Statements: All patterns are structures. All structures are ideas. Conclusions: I. All patterns are ideas. II. Some ideas are patterns.
Venn Diagram Method:
Draw three circles for patterns, structures, and ideas.

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

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

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

Answer: Both conclusions I and II follow

Question 20

Statements: All fish are vertebrates. All vertebrates are birds. Conclusions: I. All fish are birds. II. Some birds are fish.
Venn Diagram Method:
Draw three circles for fish, vertebrates, and birds.

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

Analytical Method (A + A = A):
All fish are vertebrates (A) + All vertebrates are birds (A) = All fish are birds (A)

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

Answer: Both conclusions I and II follow
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