"Writing subsets"

Subsets and Their Properties

• Definition of a Subset: A subset of a set is any set that contains only elements from the parent set or is the empty set.

• Subset Examples: For any set, the subsets can be listed in roster form. Each subset can include:

  • An empty set (∅): Contains no elements.
  • The set itself: Always a subset (e.g., if we have a set S = {6, 5}, then S is a subset of S).

• Listing Subsets:

  • If a set contains elements, its subsets can be categorized based on the number of elements they have.
    • Subsets with 0 elements: ∅
    • Subsets with 1 element: {6}, {5}
    • Subsets with 2 elements: {6, 5}

• Total Number of Subsets: The total number of subsets of a set with n elements can be computed using the formula:
  2^n

  • For a set with two elements like {6, 5}, the total number of subsets is:
  • n = 2, hence total subsets = 2^2 = 4 (which includes ∅, {6}, {5}, {6, 5}).

• Important Note: The empty set is a unique subset of any set while every set is a subset of itself.

• Final Listing - Example Set:
  Given the set {6, 5}, the complete subset listing will be:

  1. ∅
  2. {6}
  3. {5}
  4. {6, 5}