Practice Venn Diagram in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A diagram using overlapping circles to visually represent sets and their relationships such as union, intersection, and complement.

Each circle represents a set; overlapping regions show shared elements; the rectangle border is the universal set.

Showing a random 20 of 50 problems.

Example 1

easy

In a Venn diagram with universe

U

drawn as a rectangle, what does the region OUTSIDE both circles represent?

Example 2

easy

If circle

A

is drawn entirely inside circle

B

in a Venn diagram, what relationship holds?

Example 3

medium

A Venn diagram has 'A only' =

2x

, overlap =

x

, 'B only' =

3x

. If

|A \cup B| = 36

, find

x

Example 4

medium

A Venn diagram shows: only

A=10

, only

B=8

, both

=5

, neither

=7

. What is the total number of elements in the universe?

Example 5

easy

In a Venn diagram, which region is 'in

A

but not in

B

Example 6

easy

Use inclusion–exclusion:

|A|=12,\ |B|=9,\ |A\cap B|=4

. Find

|A\cup B|

Example 7

challenge

A three-circle Venn diagram has

|A|=|B|=|C|=20

, each pairwise overlap (total)

=8

, and all three

=3

. Find the number in exactly one circle.

Example 8

easy

If sets

A

and

B

are disjoint, how do their circles look in a Venn diagram?

Example 9

medium

Which region in a Venn diagram represents

(A \cup B)^c

Example 10

medium

Two circles overlap in a Venn diagram. Does the overlap GUARANTEE the sets share elements?

Example 11

easy

In a class of 25,

13

play soccer,

11

play basketball,

4

play both. How many play only soccer?

Example 12

easy

A Venn diagram shows 5 in 'A only', 3 in the overlap, 4 in 'B only'. How many are in

A \cup B

Example 13

challenge

Three sets

A,B,C

satisfy

|A\cap B|+|A\cap C|+|B\cap C|=42

and

|A\cap B\cap C|=10

. How many elements lie in exactly two of the three sets?

Example 14

medium

In a class of 30, a Venn diagram shows 14 take art, 18 take music, 6 take both. How many take art only?

Example 15

medium

A Venn diagram shows 'A only'

=6

, overlap

=4

, 'B only'

=5

. Find

|A \cap B|

Example 16

medium

Three-circle Venn diagram: the very center region represents which set operation on

A

B

C

Example 17

medium

|A \cup B| = 30

|A| = 22

|B| = 17

. Find

|A \cap B|

Example 18

medium

Given

|A| = 20

|B| = 15

|A \cup B| = 28

, find

|A \cap B|

using the inclusion-exclusion principle.

Example 19

medium

A Venn diagram for

A

and

B

has 'A only'

=x

, overlap

=7

, 'B only'

=9

, and

|A|=15

. Find

x

Example 20

easy

A Venn diagram has 'A only'

= 7

, overlap

= 4

, 'B only'

= 6

. Find

|A|

← Back to Venn Diagram Worked Examples Formula Explained

Related Concepts

Set Union Intersection