Let Y = {0, 1, 2, 3}. (a) Show that Y^ω, the set of all sequences f : N → Y, is uncountable. (b) Show that the set of all sequences of natural numbers g : N → N is an uncountable set.

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Q: (ii) for every singleton set A, m* (A) = 0.

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Q: (e) If each fn has at most a countable number of discontinuities, then f hasat most a countable…

A: Consider the example: fnx=1q             x= pqwith p,q∈N, gcdp,q=1,q≤n0             otherwise So,…

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A: 1) is false and 2) is true.

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A: First we show that the interval S={(a,b):a,b∈Q∪{+∞,−∞}} is countableWe know that, Since Q is…

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A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

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Q: of the cantor Show That measure set C is Zero.

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A: Kindly refer to Step 2 for the solution.

Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

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A: Let  be any set , then

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Q: (a) |([10]² – {1,3} × {2, 5, 6}) — {5, 7, 9} × {8, 10}|.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Show that the set of all [a,b] with a&lt;=b is also countable Show that the set of all (a,b] with…

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Q: Define dircect proof

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A: Given Information: U=1,2,3,4,5,6,7,8,9 A=n∈U | n is odd B=n∈U | 2n+1 is a prime number

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