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Set Language and Notation

  • A well-defined collection of objects is called a set and each object is called a member or element of the set
  • A set is denoted by a capital letter and is expressed by:
    • Listing its elements, e.g. V = {a, e, i, o, u}, or
    • A set builder notation:
      • R – set of real numbers
      • R+ – set of positive real numbers
      • N – set of natural numbers
      • Z – set of integers
      • Z+ – set of positive integers
      • E.g. {x: x is a prime number and x < 30}
  • For any finite set P, n(P) denotes the number of elements in P
  • A null or empty set is denoted by {} or ø
  • For any two sets P and Q:
    • P = Q if they have the same elements
    • P ⊆ Q if x ∈ P ⇒ x ∈ Q
    • P ∩ Q = {x: x ∈ P and x ∈ Q}
    • P ∩ Q = ø then P and Q are disjoint sets
    • P ∪ Q = {x: x ∈ P or x v Q}
  • For any set P and universal set ξ
    • P ⊆ ξ and 0 ≤ n(P) ≤ n(ξ)
    • P’ = {x: x ∈ ξ and x ∉ P}
    • P ∩ P’ = ø
    • P ∪ P’ = ξ
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