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Venn Diagram

General Intelligence & Reasoning · Logic & Analytical Reasoning

Useful for: SSC CGL, Railway RRB, OSSC RHT — Regular High School Teacher, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Arts, OSEPA Upper Primary — Science, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts

and 2 more exams

OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM

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Overview

Venn questions show how groups overlap; cube questions use opposite faces and painted-cube counting; paper folding tracks holes through unfolding.

Key points

Subset: one circle inside another (cats ⊂ animals); overlap: some members common (doctors, women); separate: no common member (cats, dogs).
In a standard die, opposite faces are not shown together on one view.
A cube cut into n³ small cubes with all faces painted: 3 faces painted = 8, two = 12(n − 2), one = 6(n − 2)², none = (n − 2)³.
Each unfold doubles holes, mirrored across the fold line.
Count regions in Venn questions carefully: numbers in overlaps belong to both sets.

Explanation

Two views of a die sharing a face: the faces in the same relative positions are opposite.
For a 4 × 4 × 4 cube, two-face painted = 12 × 2 = 24.
Holes near the fold line mirror to the same distance on the other side.
Use a quick sketch for three-set Venn diagrams.

Step by step

Identify the type.
Apply the rule or formula.
Sketch to confirm.

Examples

Doctors, Women, Mothers → overlapping circles with mothers inside women and partly overlapping doctors.
A painted cube cut into 27 small cubes: exactly two faces painted = 12 × 1 = 12.
A square sheet folded once with one hole punched gives two holes symmetric about the fold.

Traps and advanced points

Trap: Treating overlap groups as subsets.
Trap: Assuming adjacent faces are opposite.
Trap: Forgetting to mirror holes.

Quick revision

8 corners, 12(n−2) edges, 6(n−2)² faces.
Unfold doubles holes.
Subset vs overlap vs separate.

Practice MCQs

All writers are workers. Some writers are experienced. Which conclusion definitely follows?
1. Some experienced people are workers
2. All workers are writers
3. No writers are experienced
4. All experienced people are writers
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Answer: (a) Some experienced people are workers. If some A are experienced and all A are B, then some experienced are B.
If the sets “Artists” and “Travelers” overlap partly, which statement best describes the Venn diagram?
1. All artists are travelers
2. Some artists may be travelers
3. No artists can be travelers
4. All travelers are artists
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Answer: (b) Some artists may be travelers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Athletes” and “Volunteers” overlap partly, which statement best describes the Venn diagram?
1. All athletes are volunteers
2. Some athletes may be volunteers
3. All volunteers are athletes
4. No athletes can be volunteers
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Answer: (b) Some athletes may be volunteers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Doctors” and “Voters” overlap partly, which statement best describes the Venn diagram?
1. All voters are doctors
2. No doctors can be voters
3. All doctors are voters
4. Some doctors may be voters
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Answer: (d) Some doctors may be voters. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Farmers” and “Cyclists” overlap partly, which statement best describes the Venn diagram?
1. All cyclists are farmers
2. All farmers are cyclists
3. Some farmers may be cyclists
4. No farmers can be cyclists
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Answer: (c) Some farmers may be cyclists. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Lawyers” and “Researchers” overlap partly, which statement best describes the Venn diagram?
1. All researchers are lawyers
2. All lawyers are researchers
3. Some lawyers may be researchers
4. No lawyers can be researchers
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Answer: (c) Some lawyers may be researchers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Doctors” and “Designers” overlap partly, which statement best describes the Venn diagram?
1. Some doctors may be designers
2. All designers are doctors
3. All doctors are designers
4. No doctors can be designers
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Answer: (a) Some doctors may be designers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Nurses” and “Researchers” overlap partly, which statement best describes the Venn diagram?
1. All nurses are researchers
2. All researchers are nurses
3. No nurses can be researchers
4. Some nurses may be researchers
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Answer: (d) Some nurses may be researchers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Engineers” and “Cyclists” overlap partly, which statement best describes the Venn diagram?
1. No engineers can be cyclists
2. Some engineers may be cyclists
3. All engineers are cyclists
4. All cyclists are engineers
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Answer: (b) Some engineers may be cyclists. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Doctors” and “Musicians” overlap partly, which statement best describes the Venn diagram?
1. No doctors can be musicians
2. Some doctors may be musicians
3. All doctors are musicians
4. All musicians are doctors
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Answer: (b) Some doctors may be musicians. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Lawyers” and “Volunteers” overlap partly, which statement best describes the Venn diagram?
1. All volunteers are lawyers
2. No lawyers can be volunteers
3. Some lawyers may be volunteers
4. All lawyers are volunteers
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Answer: (c) Some lawyers may be volunteers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Artists” and “Singers” overlap partly, which statement best describes the Venn diagram?
1. All artists are singers
2. No artists can be singers
3. All singers are artists
4. Some artists may be singers
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Show answer
Answer: (d) Some artists may be singers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Athletes” and “Graduates” overlap partly, which statement best describes the Venn diagram?
1. All athletes are graduates
2. All graduates are athletes
3. No athletes can be graduates
4. Some athletes may be graduates
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Answer: (d) Some athletes may be graduates. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Lawyers” and “Cyclists” overlap partly, which statement best describes the Venn diagram?
1. All lawyers are cyclists
2. No lawyers can be cyclists
3. All cyclists are lawyers
4. Some lawyers may be cyclists
Read chapter notes · Similar questions
Show answer
Answer: (d) Some lawyers may be cyclists. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Engineers” and “Travelers” overlap partly, which statement best describes the Venn diagram?
1. No engineers can be travelers
2. All engineers are travelers
3. Some engineers may be travelers
4. All travelers are engineers
Read chapter notes · Similar questions
Show answer
Answer: (c) Some engineers may be travelers. Partial overlap means intersection exists but neither set fully contains the other.