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Basic All-All Syllogism - Expert Level: four-term elimination Basic All-All Syllogism EXPERT

This skill evaluation ⚡ worksheet focuses on Basic All-All Syllogism - a key topic in Syllogism. You'll solve 20 expert-level problems (Worksheet 9 of 10). The primary focus is on four-term elimination. Master basic all-all syllogism ssc cgl, basic all-all syllogism reasoning tricks, and fast basic all-all syllogism solving through systematic practice.

📝 Worksheet 9 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Basic All-All Syllogism
Worksheet 9 of 10 (88% complete)

Question 1

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

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

Analytical Method (A + A = A):
All pharmacists are musicians (A) + All musicians are entrepreneurs (A) = All pharmacists are entrepreneurs (A)

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

Answer: Both conclusions I and II follow

Question 2

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

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

Analytical Method (A + A = A):
All processes are systems (A) + All systems are methods (A) = All processes are methods (A)

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

Answer: Both conclusions I and II follow

Question 3

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

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

Analytical Method (A + A = A):
All concepts are methods (A) + All methods are strategies (A) = All concepts are strategies (A)

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

Answer: Both conclusions I and II follow

Question 4

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

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

Analytical Method (A + A = A):
All valuable are beautiful (A) + All beautiful are accessible (A) = All valuable are accessible (A)

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

Answer: Both conclusions I and II follow

Question 5

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

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

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

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

Answer: Both conclusions I and II follow

Question 6

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

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

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

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

Answer: Both conclusions I and II follow

Question 7

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

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

Analytical Method (A + A = A):
All wild are reptiles (A) + All reptiles are fish (A) = All wild are fish (A)

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

Answer: Both conclusions I and II follow

Question 8

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

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

Analytical Method (A + A = A):
All omnivores are domestic (A) + All domestic are vertebrates (A) = All omnivores are vertebrates (A)

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

Answer: Both conclusions I and II follow

Question 9

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

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

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

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

Answer: Both conclusions I and II follow

Question 10

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

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

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

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

Answer: Both conclusions I and II follow

Question 11

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

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

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

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

Answer: Both conclusions I and II follow

Question 12

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

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

Analytical Method (A + A = A):
All devices are furniture (A) + All furniture are utensils (A) = All devices are utensils (A)

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

Answer: Both conclusions I and II follow

Question 13

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

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

Analytical Method (A + A = A):
All patterns are processes (A) + All processes 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 14

Statements: All omnivores are mammals. All mammals are nocturnal. Conclusions: I. All omnivores are nocturnal. II. Some nocturnal are omnivores.
Venn Diagram Method:
Draw three circles for omnivores, mammals, and nocturnal.

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

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

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

Answer: Both conclusions I and II follow

Question 15

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

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

Analytical Method (A + A = A):
All frameworks are systems (A) + All systems are ideas (A) = All frameworks are ideas (A)

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

Answer: Both conclusions I and II follow

Question 16

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

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

Analytical Method (A + A = A):
All herbivores are amphibians (A) + All amphibians are warm-blooded (A) = All herbivores are warm-blooded (A)

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

Answer: Both conclusions I and II follow

Question 17

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

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

Analytical Method (A + A = A):
All artists are pilots (A) + All pilots are athletes (A) = All artists are athletes (A)

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

Answer: Both conclusions I and II follow

Question 18

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

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

Analytical Method (A + A = A):
All birds are diurnal (A) + All diurnal are domestic (A) = All birds are domestic (A)

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

Answer: Both conclusions I and II follow

Question 19

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

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

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

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

Answer: Both conclusions I and II follow

Question 20

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

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

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

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

Answer: Both conclusions I and II follow
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