Venn Diagrams — Practice

Question 1

Which relationship best represents: Table, Chair, Furniture?
(a) Three separate circles (b) Three overlapping circles (c) Furniture enclosing two separate circles (d) Furniture inside Table

Accepted Answer

(c) Furniture enclosing two separate circles.

Tables and chairs are both furniture but never each other, so both sit as separate circles inside Furniture.

Question 2

In a class of 100, 60 play cricket, 40 play football and 20 play both. How many play neither?
(a) 10 (b) 15 (c) 20 (d) 25

Accepted Answer

(c) 20.

At least one = 60 + 40 − 20 = 80, so neither = 100 − 80 = 20.

Question 3

40 people know English, 30 know Hindi and 15 know both. How many know only English?
(a) 20 (b) 25 (c) 30 (d) 15

Accepted Answer

(b) 25.

Only English = 40 − 15 = 25.

Question 4

In a group, 30 like tea, 25 like coffee and 10 like both. How many like tea or coffee?
(a) 40 (b) 45 (c) 50 (d) 55

Accepted Answer

(b) 45.

30 + 25 − 10 = 45.

Question 5

Which relationship best represents: India, Asia, World?
(a) Three separate circles (b) India ⊂ Asia ⊂ World (nested) (c) Three overlapping circles (d) World ⊂ Asia ⊂ India

Accepted Answer

(b) India ⊂ Asia ⊂ World (nested).

India is part of Asia, which is part of the World — concentric containment.

Question 6

Which relationship best represents: Earth, Sun, Moon?
(a) Three separate circles (b) Nested circles (c) Two overlapping, one separate (d) Three overlapping circles

Accepted Answer

(a) Three separate circles.

They are distinct bodies with no class membership overlap, so three disjoint circles.

Question 7

In a survey of 60 people: 25 read A, 26 read B, 26 read C; 9 read A and B, 11 read B and C, 8 read A and C, and 3 read all three. How many read at least one newspaper?
(a) 48 (b) 50 (c) 52 (d) 54

Accepted Answer

(c) 52.

25 + 26 + 26 − 9 − 11 − 8 + 3 = 77 − 28 + 3 = 52.

Question 8

Using the same survey (60 people; at least one = 52), how many read none of the three newspapers?
(a) 6 (b) 7 (c) 8 (d) 9

Accepted Answer

(c) 8.

None = total − at least one = 60 − 52 = 8.

Question 9

Which relationship best represents: Doctors, Engineers, Married people?
(a) Three separate circles (b) Nested circles (c) Three mutually overlapping circles (d) Two separate, one enclosing

Accepted Answer

(c) Three mutually overlapping circles.

A person can be a doctor and married, an engineer and married, etc., so all three classes intersect.

Practice — Venn Diagrams

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