For any subset A of R, define the function XA : R → R by [1, XA(x) = 0, if π A if x ¢ A. Show that if A is measurable, then XA is a measurable function.

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A: Solution:-

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A: We will use basic concepts of logical equivalence here

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A: This is a problem of topology.

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A: Given  2ydx + (3y - 2x)dy = 0

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A: This a question of propositional logic.

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A: Given that 3&lt;r&lt;6, 65°&lt;θ&lt;95°, 50°&lt;φ&lt;80°

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A: This is the problem of Reiman Sum.

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A: We will use the basic knowledge of curve fitting by the "least square approximations" method.

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A: Bisection method

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