Universal Set

The universal set is the set that contains all objects under consideration in a particular discussion or context.

• Notation: $U$ (common)
• Example:
  • If working with natural numbers, $U=\mathbb{N}$
  • If working with letters in the English alphabet, $U=\{a,b,\dots ,z\}$
• Properties:
  • Every set in the discussion is a Subset of $U:A\subseteq U$
  • Complement of a set $A$ is relative to $U$: $A^c=U\text{A}$