General Mental Ability – Venn diagrams

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: General Mental Ability

Sub-Topic: Venn Diagrams

Each question tests your ability to interpret relationships between sets using Venn-diagram logic. Choose the most appropriate answer.

Venn Diagram MCQs

MCQ 1

All doctors are educated. Some educated people are teachers. Which conclusion is correct?
A. All teachers are doctors
B. Some doctors may be teachers
C. No teacher is a doctor
D. All educated are doctors

Correct Answer: B
Explanation: Doctors ⊂ Educated; Teachers overlap with Educated → possible overlap with Doctors.

MCQ 2

All pens are books. Some books are bags. Which diagram fits best?
A. Three separate circles
B. Pens inside books; books overlap bags
C. Books inside pens
D. Bags inside pens

Correct Answer: B
Explanation: Pens are a subset of books; some books overlap with bags.

MCQ 3

No cat is a dog. Some dogs are pets. Which conclusion is valid?
A. Some pets are cats
B. No pet is a cat
C. Some pets are dogs
D. All dogs are cats

Correct Answer: C
Explanation: “Some dogs are pets” directly implies some pets are dogs.

MCQ 4

All fruits are healthy. All apples are fruits. What is correct?
A. All apples are healthy
B. Some healthy are apples
C. No apple is healthy
D. Some fruits are not healthy

Correct Answer: A
Explanation: Apples ⊂ Fruits ⊂ Healthy.

MCQ 5

Some boys are girls. Some girls are students. Which is correct?
A. All boys are students
B. Some boys may be students
C. No boy is a student
D. All students are boys

Correct Answer: B
Explanation: Overlap of boys–girls and girls–students allows boys–students overlap.

MCQ 6

All chairs are furniture. No furniture is vehicle. Which is true?
A. Some chairs are vehicles
B. No chair is a vehicle
C. All vehicles are chairs
D. Some furniture are vehicles

Correct Answer: B
Explanation: Chairs ⊂ Furniture and Furniture ∩ Vehicle = ∅.

MCQ 7

Which diagram represents: Some A are B, all B are C?
A. A and B separate, both inside C
B. B inside C, A overlapping B
C. A inside B inside C
D. All three separate

Correct Answer: B
Explanation: Only part of A overlaps B; B fully inside C.

MCQ 8

All politicians are leaders. Some leaders are honest. Which is correct?
A. All politicians are honest
B. Some politicians may be honest
C. No politician is honest
D. All honest are politicians

Correct Answer: B
Explanation: Possible overlap between politicians and honest leaders.

MCQ 9

No man is immortal. All kings are men. Which follows?
A. Some kings are immortal
B. No king is immortal
C. Some men are immortal
D. All immortals are kings

Correct Answer: B
Explanation: Kings ⊂ Men; Men ∩ Immortal = ∅.

MCQ 10

Some teachers are writers. All writers are creative. Which is correct?
A. Some teachers are creative
B. All teachers are creative
C. No teacher is creative
D. Some creative are not writers

Correct Answer: A
Explanation: Teachers ∩ Writers ⊂ Creative.

MCQ 11

All rivers are water bodies. Some water bodies are polluted. Which is true?
A. Some rivers are polluted
B. All polluted are rivers
C. Some polluted may be rivers
D. No river is polluted

Correct Answer: C
Explanation: Possible overlap but not guaranteed.

MCQ 12

All engineers are graduates. Some graduates are unemployed. Which is valid?
A. All engineers are unemployed
B. Some engineers may be unemployed
C. No engineer is unemployed
D. All unemployed are engineers

Correct Answer: B
Explanation: Possible overlap via graduates.

MCQ 13

Which relationship shows three mutually exclusive sets?
A. Teacher–Student–Human
B. Cat–Dog–Bird
C. Apple–Fruit–Food
D. Square–Rectangle–Shape

Correct Answer: B
Explanation: Cats, dogs, and birds are distinct categories.

MCQ 14

All laptops are computers. Some computers are expensive. Which conclusion follows?
A. All laptops are expensive
B. Some laptops may be expensive
C. No laptop is expensive
D. All expensive are laptops

Correct Answer: B
Explanation: Possible overlap between laptops and expensive computers.

MCQ 15

No tree is animal. All animals are living beings. Which is correct?
A. Some trees are animals
B. No tree is a living being
C. No animal is a tree
D. All trees are animals

Correct Answer: C
Explanation: Given directly by the first statement.

MCQ 16

Some students are athletes. All athletes are healthy. Which is correct?
A. All students are healthy
B. Some students are healthy
C. No student is healthy
D. All healthy are students

Correct Answer: B
Explanation: Students ∩ Athletes ⊂ Healthy.

MCQ 17

Which diagram fits: All A are B, all B are C?
A. A inside B inside C
B. B inside A inside C
C. C inside B inside A
D. All separate

Correct Answer: A
Explanation: Transitive subset relation.

MCQ 18

No pen is pencil. Some pencils are erasers. Which is valid?
A. Some erasers are pens
B. No eraser is pen
C. Some erasers are pencils
D. All pens are erasers

Correct Answer: C
Explanation: Direct restatement of “some pencils are erasers”.

MCQ 19

All doctors are professionals. All professionals are respected. Which follows?
A. All doctors are respected
B. Some respected are doctors
C. Both A and B
D. Neither A nor B

Correct Answer: C
Explanation: Doctors ⊂ Professionals ⊂ Respected.

MCQ 20

Some cars are electric. No electric vehicle is noisy. Which is correct?
A. Some cars are noisy
B. No electric car is noisy
C. All cars are electric
D. Some noisy are electric

Correct Answer: B
Explanation: Electric vehicles ∩ Noisy = ∅.

MCQ 21

All books are knowledge. Some knowledge is power. Which is correct?
A. All books are power
B. Some books may be power
C. No book is power
D. All power is book

Correct Answer: B
Explanation: Possible overlap only.

MCQ 22

Which relation shows complete overlap?
A. Doctors and engineers
B. Writers and poets
C. Square and rectangle
D. Dogs and cats

Correct Answer: C
Explanation: All squares are rectangles.

MCQ 23

Some fruits are sweet. All sweet things are tasty. Which is correct?
A. All fruits are tasty
B. Some fruits are tasty
C. No fruit is tasty
D. All tasty are fruits

Correct Answer: B
Explanation: Fruits ∩ Sweet ⊂ Tasty.

MCQ 24

No metal is wood. Some woods are furniture. Which is valid?
A. Some furniture are metal
B. No metal is furniture
C. Some furniture are wood
D. All metals are furniture

Correct Answer: C
Explanation: Direct from second statement.

MCQ 25

All teachers are educated. Some educated are unemployed. Which follows?
A. All teachers are unemployed
B. Some teachers may be unemployed
C. No teacher is unemployed
D. All unemployed are teachers

Correct Answer: B
Explanation: Possible overlap through educated set.

MCQ 26

Which diagram best represents: No A is B, some B are C?
A. A separate; B overlapping C
B. A inside B; C separate
C. B inside A; C overlapping A
D. All overlapping

Correct Answer: A
Explanation: A and B are disjoint; B overlaps C.

MCQ 27

All newspapers are printed. Some printed are magazines. Which is correct?
A. Some newspapers are magazines
B. Some magazines are newspapers
C. Some printed may be newspapers
D. All magazines are newspapers

Correct Answer: C
Explanation: Newspapers ⊂ Printed → some printed are newspapers.

MCQ 28

All lions are animals. No animal is a plant. Which follows?
A. Some lions are plants
B. No lion is a plant
C. All plants are lions
D. Some animals are plants

Correct Answer: B
Explanation: Lions ⊂ Animals; Animals ∩ Plants = ∅.

MCQ 29

Some employees are graduates. Some graduates are managers. Which is correct?
A. All employees are managers
B. Some employees may be managers
C. No employee is manager
D. All managers are employees