Given a set ω, let p(ω) denote the the power set of ω, that is p(ω) is the collection of all subsets of ω. prove that ω and p(ω) do not have the same cardinality. hint: given a function φ : ω → p(ω), consider the set x : = {ω ∈ ω : ω /∈ φ(ω)}.