Answer the following true or false and prove all your assertions. (a) Every Cauchy sequence of rational numbers converges to a rational number. (b) Every function that is continuous at π is differentiable at T. (c) if A and B are sets, then (AUB) = An Bc. (d) If {x} is a sequence in the interval (a, b], then there must be a subsequence that converges to a point of (a, b].

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