Disjoint and Partition

• Two sets $A$ and $B$ are disjoint if $A\cap B = \emptyset$

• A collection of sets $\{A_1,A_2,...,A_n\}$ is a partition of $\Omega$ if:

  1. Disjoint: $A_i \cap A_j = \emptyset$
  2. Decompose: $\bigcup_{i=1}^n A_i = \Omega$

• This is important because it allows us to decompose $\Omega$ into smaller subsets to analyze separately.

Example $\{1,3,4\}$, $\{4,5\}$ and $\{6\}$ form a partition of $\{1,2,3,4,5,6\}$