Set Theory

Basics

  • A ⊆ B = A is a subset of B. All the members of A are also found in B
  • A ∪ B = Union. All the elements that are in A, B or both
  • A ∩ B = Intersection. All the elements that are both in A and B
  • A⊂ = Complement or Absolute complement. The set of all elements that are not in A but are in U, which is the universal set, basically a superset of all sets defined
  • A⊂ ∩ B = Relative complement. The set of elements that are not in A nor in A ∩ B
  • A ∆ B = Symmetric difference. The set of elements that is in either one of the sets, but not in both
  • A x B = Cartesian product. The set whose elements are all the ordered pairs of A and B. Like A = {1,2,3} and B = {4,5,6} will result in a Cartesian product of {% raw %} {{1,4}, {1,5}, {1,6}, {2,4}, {2,5}, {2,6}, {3,4}, {3,5}, {3,6}}{% endraw %}