Establish whether the following propositions are true or false. Provide a formal proof for just one among the true propositions and suitable counterexamples for all false propositions. a.) A convergent sequence in R" is a Cauchy sequence. b.) If a correspondence is Upper Hemicontinuous, then it has the closed graph property. c.) Let V and U be two vector spaces over the same field K and let l be a linear function l: V →U. The set Iml is a vector subspace of U.

Q: Exercise 3. Let x € R. If x > 1, prove by induction that r" >x for every integer n > 2. If 0 2.

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A: To Prove: The Cantor-Schroeder-Bernstein Theorem.

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