1.4 Power Sets

Sets

Power Set

• $\mathcal{P}(A)$ = { S: S $\subseteq$ A} ⇒ power set is the set of all subsets
  • E.g. A = { 1, 2 }, $\mathcal{P}(A)$ = { $\varnothing$, { 1 }, { 2 }, { 1, 2 } }

Fact

• If A is a finite set, then,
  • |$\mathcal{P}(A)$| = 2 ${}^{|A|}$ .