Terms & Definitions

  • Compliment: $S^c$ takes the exact opposite of the set it's acting on. A complimented compliment makes no compliment at all.
  • DeMorgan's Rule: An equivalent statement of set operators can be found by complimenting each set, flipping the operators, and complimenting the final output.
  • Intersection Operator: The intersection operator $\cap$, finds only the elements in common between two sets. This is the same as the logical AND function
  • Sample Space: The sample space, denoted as $S$ is a set of all possible outcomes of an event. It can either be a list, like $S=\{ 1,2,4,8\}$, or a property, or list or properties that defines and fully constrains a variable. An example of the latter is $S=\{ x:x \text{ is even and } 0\leq{x}\leq{10}\}$ or $S=\{ (x,y): x+y=1, 0\leq{x}\leq{1},0\leq{y}\leq{1}\}$
  • Union Operator: The union operator, $\cup$, combines to sets together - but keep in mind it does not repeat elements which are common between the two sets. This is the same as a logical OR function.