Venn Diagrams and Set Operations

• A Venn diagram is used to represent a set.
• Draw a rectangle to represent the universal set
• Draw circles inside to represent subsets.
• U = {1,2,3,4,5,6}, A = {1,2,3}, B = {2,4,6} draw this.
• Draw the four possible ways to look at two sets.
  • A = B
  • A⊂B
  • disjoint
  • A⊄B and B⊄A;
• Label with Roman Numerals I, II and III
• The Complement of a set A, written A' is the set of all elements in U not in A.
• From the previous example, find A' = {4,5,6}
• The intersection of two sets, A and B, written A∪B is the set of all elements common to both sets.
• A ∪B = {2}
• and normally means intersection.
• The union of two sets, A and B, written A∩B, is the set of all element is set a or in set b. A∪B = {1,2,3,4,6}
• or normally means union.
• 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 elements in A which are not in B.
• A-B = {1,3}