🪴 Notes

Set Operations

1 min read

Course: CSCI 1900

Union (or)

  • Denoted with 𝐴∪𝐵
  • {𝑥|𝑥∈𝐴or𝑥∈𝐵}

Intersection (and)

  • Denoted with 𝐴∩𝐵
  • {𝑥|𝑥∈𝐴and𝑥∈𝐵}
  • If the intersections are empty, then 𝐴 and 𝐵 are disjoint

Difference

  • Denoted with 𝐴−𝐵
  • {𝑥|𝑥∈𝐴and𝑥∉𝐵}
  • Every element of 𝐴 that is not also an element in 𝐵

Complement

  • Denoted with 𝐴
  • {𝑥∈𝑈|𝑥∉𝐴}
  • All elements in universal set that are not in 𝐴

Symmetric Difference

  • Denoted with 𝐴⊕𝐵
  • {𝑥|𝑥∈𝐴and𝑥∉𝐵or𝑥∈𝐵and𝑥∉𝐴}
  • The elements that are in either 𝐴 or 𝐵 but not in both (exclusive or)

Order of Operations

  1. Parenthesis
  2. Complements
  3. Intersections, unions, differences (→)

Example

  • (𝐴∪𝐵)∩𝐶
    • 𝑈={1,2,3,4,5,6}
    • 𝐴={1,2,3}
    • 𝐵={2,3,4}
    • 𝐶={1,3,5}
  • 𝐵→{1,5,6}
  • 𝐴∪{1,5,6}→{1,2,3,5,6}
  • {1,2,3,5,6}∩𝐶→{1,3,5}

Graph View