Subsets

• A set S is a subset of set B, written as S ⊆ B, if every element s ∈ S, s ∈ B.
  • A = {a, b, c, d, e, f}, B = { a, b, c}, C = { f, e, d, c, b, a}
  • A ⊆ C, C ⊆ A
  • B ⊆ A, A ⊈ B
  • Can you give a set D such that A ⊆ D
  • Can you give another set E, such that E ⊆ A
• A set A is a proper subset of set B, written A ⊂ B, if A ⊆ B and A ≠ B.
  • A = {a, b, c, d, e, f}, B = { a, b, c}, C = { f, e, d, c, b, a}
  • A ⊄ B
  • A ⊄ C
  • B ⊂ A
  • Can you give another subset F which is a proper subset of A.
  • Can you give a subset G such that A is a proper subset of G.
• Remember
  • ∈ asks if an element is in a set
  • ⊂ and ⊆ asks the relationship between two sets.
  • 3 ∈ { 1, 2, 3}
  • {3} ⊄ { 1, 2, 3}
  • {3} ⊂ {1, 2, 3}
  • 3 ⊄ {1, 2, 2}
• if n(A)= k, there are 2^k distinct subsets of a.
  • A = {}, n(A) = ?, subsets:
  • B = {x}, n(B) = ?, subsets:
  • C = {*,+}, n(C) = ?, subsets: