5/18 TIL: Cartesian Product

• Cartesian Product A X B is the set of all ordered pairs (a,b) where a ∈ A and b ∈ B
• A function:
  • For every input, there is some output
  • Has one output at most for an input—vertical line testing could be done to test this
• A function F between A and B is a relation between A and B (subset of A X B)—define this using the Cartesian Product:
  • For every element x ∈ A there is an element y ∈ b such that (x, y) ∈ F
  • If (x, y) ∈ F and (x, z) ∈ F then y = z
• Two statements are logically equivalent if they have the same truth table
  • p ≡ ~(~p) (p equals to not not p)
  • DeMorgan's Laws