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

Example 2

easy
If circle AA is drawn entirely inside circle BB in a Venn diagram, what relationship holds?

Example 3

medium
A Venn diagram has 'A only' = 2x2x, overlap = xx, 'B only' = 3x3x. If ∣A∪B∣=36|A \cup B| = 36, find xx.

Example 4

medium
A Venn diagram shows: only A=10A=10, only B=8B=8, both =5=5, neither =7=7. What is the total number of elements in the universe?

Example 5

easy
In a Venn diagram, which region is 'in AA but not in BB'?

Example 6

easy
Use inclusion–exclusion: ∣A∣=12, ∣B∣=9, ∣A∩B∣=4|A|=12,\ |B|=9,\ |A\cap B|=4. Find ∣A∪B∣|A\cup B|.

Example 7

challenge
A three-circle Venn diagram has ∣A∣=∣B∣=∣C∣=20|A|=|B|=|C|=20, each pairwise overlap (total) =8=8, and all three =3=3. Find the number in exactly one circle.

Example 8

easy
If sets AA and BB are disjoint, how do their circles look in a Venn diagram?

Example 9

medium
Which region in a Venn diagram represents (A∪B)c(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, 1313 play soccer, 1111 play basketball, 44 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∪BA \cup B?

Example 13

challenge
Three sets A,B,CA,B,C satisfy ∣A∩B∣+∣A∩C∣+∣B∩C∣=42|A\cap B|+|A\cap C|+|B\cap C|=42 and ∣A∩B∩C∣=10|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=6, overlap =4=4, 'B only' =5=5. Find ∣A∩B∣|A \cap B|.

Example 16

medium
Three-circle Venn diagram: the very center region represents which set operation on AA, BB, CC?

Example 17

medium
∣A∪B∣=30|A \cup B| = 30, ∣A∣=22|A| = 22, ∣B∣=17|B| = 17. Find ∣A∩B∣|A \cap B|.

Example 18

medium
Given ∣A∣=20|A| = 20, ∣B∣=15|B| = 15, ∣A∪B∣=28|A \cup B| = 28, find ∣A∩B∣|A \cap B| using the inclusion-exclusion principle.

Example 19

medium
A Venn diagram for AA and BB has 'A only' =x=x, overlap =7=7, 'B only' =9=9, and ∣A∣=15|A|=15. Find xx.

Example 20

easy
A Venn diagram has 'A only' =7= 7, overlap =4= 4, 'B only' =6= 6. Find ∣A∣|A|.
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Related Concepts

SetUnionIntersection