Worksheet: Disjoint Sets

In this worksheet, we will practice using Venn diagrams to identify and describe disjoint sets and their corresponding known facts.


Using the Venn diagram below, find 𝑋𝑌.

  • A{4,2,6}
  • B
  • C{5,8,3,7}
  • D{5,8,3,7,4,2,6}


Find 𝐴𝐶 using the Venn diagram.

  • A{11,6}
  • B{8,10}
  • C
  • D{9,11,4,5,6}


Using the Venn diagram below, find {8,6,7,3}𝐴.

  • A{8,7,3}
  • B
  • C{6}
  • D{8,7}


Which Venn Diagram shows that 𝑋 and 𝑌have no elements in common?

  • A(c)
  • B(b)
  • C(d)
  • D(a)


Using the Venn diagram below, find {8,6,7,5,3}𝐴.

  • A
  • B{8,6,7}
  • C{5}
  • D{5,3}
  • E{8,6,5,3}


Using the Venn diagram below, find 𝑋𝑌.

  • A{3,8,7}
  • B
  • C{4,1,2}
  • D{4,1,2,3,8,7}


Fill in the blank: If 𝐴=𝜙 and 𝐵=𝜙, then 𝐴 and 𝐵 are .

  • Aintersected
  • Bdisjoint


What are the disjoint sets in the following Venn diagram?

  • AThere are no disjoint sets.
  • B𝑋 and 𝑍
  • C𝑌 and 𝑍
  • D𝑋 and 𝑌


Using the following Venn diagram, choose the true statement.

  • A𝑋𝑌=𝜙
  • B𝑋𝑌=𝜙
  • C𝑌𝑋
  • D𝑋𝑌
  • E𝑋𝑌=𝜙


Use Venn diagrams to check if 𝐴={2,4,6,8,9} and 𝐵={1,3,5,7,9} are disjoint or intersected.

  • A𝐴𝐵andareintersected
  • B𝐴𝐵.andaredisjoint


Which of the following does not contain disjoint sets?

  • A
  • B
  • C
  • D


Using the given Venn diagram, decide which of the following statements is true.

  1. 𝐴 and 𝐶 are disjoint.
  2. 𝐵 and 𝐶 are disjoint.
  3. 𝐴 and 𝐵 are intersecting.
  4. There are no disjoint sets in the Venn diagram.
  • AIV only
  • BII and III
  • CIII and IV
  • DIII only
  • EI, II, and III


Choose the figure that contains disjoint sets.

  • A
  • B
  • C
  • D
  • E

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