Let G=(V, E) a graph, then show |{ € V\dg(x) = 1 mod 2}|= 0 mod 2.
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- Let E ⊂ ℝ and y ∈ ℝ. Show that E is measurable iff E + y := {x + y : x ∈ E} ismeasurable. Give a complete and detailed proof.Let E ⊂ ℝ and y ∈ ℝ. Show that E + y := {x + y : x ∈ E} is measurable then E ismeasurable. Give a complete and detailed proof.If X ∼ P oisson(λ), Prove that for any positive integer k, E[X(X − 1)(X − 2)· · ·(X − k)] = λ^ k+1
- Prove that, for every even integer n, the graph of r = sin nθ is symmetrical with respect to the x-axis.Consider E={-2+1/n} n=1 to infinity U (3,9) as a subset of R with the usual definition of < (less than) a<b is b-a is postive. Is 0 a lower bound of E?Is it possible to find a number n such that is ∫0∞ xn dxconvergent?