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)}.

(05.08a)triangle abc is transformed to similar triangle a′b′c′ below: a coordinate plane is shown. triangle abc has vertices a at 2 comma 6, b at 2 comma 4, and c at 4 comma 4. triangle a prime b prime c prime has vertices a prime at 1 comma 3, b prime at 1 comma 2, and c prime at 2 comma 2. what is the scale factor of dilation? 1 over 2 1 over 3 1 over 4 1 over 5

What is the area of a triangle with vertices at (-3 3) (-3,2) and (1,2)?

Using the figure below, select the two pairs of alternate interior angles. a: point 1 and point 4 b : point 2 and point 3 c: point 6 and point 6d: point 5 and point 7