Venn Diagrams and Set Operations

• Venn diagrams of one set.
• Venn diagrams of two sets.
  • Disjoint
  • Subsets
  • Equal Sets
  • Overlapping sets.
• Draw and number regions
• A = { 1, 2, 3, 4, 5} B = {2, 4, 6, 8, 10}, U = {1, 2, 3, ... 10}
• a ∈ X , a ∉ X
• The complement of a set A, written A', is the set of all x ∈ U and x ∉ A.
• The intersection of two sets A and B, written A∩ B, is the set of all x such that x ∈ A and x ∈ B
  • Draw the Venn diagram.
• The union of two sets A and B, written A ∪ B, is the set of all elements x such that x ∈ A or x ∈ B
• And usually means intersection and or means union.
• n(A ∪ B) ≠ n(A) + n(B).
  • Look at the Venn diagram
  • n(A ∪ B) = n(A) + n(B) - n(A ∩ B).
• The difference of two sets A and B, written A-B, is the set of all x where x ∈ A and a ∉ B.
• Do exercises page 64 on.