(D), (a) Let E = Q. Find the set of cluster points of E and prove that E is neither open %3D nor closed in R. (b) Let E = = (0, 00). Show that the set E is open in R.
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- Let A be the subset of R defined by A := (1- (((-1)^n)/n)): n ∈ N.Find all cluster points of A and justify your answerlet A be the subset of defined by A={1-((-1)/n) : n€N}. Find all cluster points of A and justify your answerLet S = { m + (-1)^(n) / n such that m,n is in all natural numbers (N) }. Find the cluster points of S.
- The mass of a 45.750g piece of copper is measured three times on two different balances with the following results: 1 45.747 1 45.76 2 45.745 2 45.77 3 45.748 3 45.74 Calculate the standard devation for each set of meaurements on each balance. Show workDoes the Identity law and closure law hold for the following: 1. Addition table for Z9 2. Multiplication table for Z9 3. The following table: x 1 2 4 5 7 8 1 1 2 4 5 7 8 2 2 4 8 1 5 7 4 4 8 7 2 1 5 5 5 1 2 7 8 4 7 7 5 1 8 4 2 8 8 7 5 4 2 1Determine the largest positive integer k such that χ(H) = χ(G) = k, where H is obtained from a nonempty graph G by subdividing each edge of G exactly once.