Worksheet: Disjoint Sets

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

Q1:

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 }

Q2:

Find 𝐴𝐶 using the Venn diagram.

  • A { 1 1 , 6 }
  • B { 8 , 1 0 }
  • C
  • D { 9 , 1 1 , 4 , 5 , 6 }

Q3:

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

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

Q4:

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

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q5:

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 }

Q6:

Using the Venn diagram below, find 𝑋𝑌.

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

Q7:

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

  • Aintersected
  • Bdisjoint

Q8:

What are the disjoint sets in the following Venn diagram?

  • AThere are no disjoint sets.
  • B 𝑋 and 𝑍
  • C 𝑌 and 𝑍
  • D 𝑋 and 𝑌

Q9:

Using the following Venn diagram, choose the true statement.

  • A 𝑋 𝑌 = 𝜙
  • B 𝑋 𝑌 = 𝜙
  • C 𝑌 𝑋
  • D 𝑋 𝑌
  • E 𝑋 𝑌 = 𝜙

Q10:

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

  • A 𝐴 𝐵 a n d a r e i n t e r s e c t e d
  • B 𝐴 𝐵 . a n d a r e d i s j o i n t

Q11:

Which of the following does not contain disjoint sets?

  • A
  • B
  • C
  • D

Q12:

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

Q13:

Choose the figure that contains disjoint sets.

  • A
  • B
  • C
  • D
  • E

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