# EXERCISES 2.2"1. Which of the following subsets of R" is open? closed? neither? Prove your answer.(a) (x :0 x< 2} CR(b) (x:x= 2 for some k eN or=0) C RXCR2y=x(g)y(h) {x: 0 |x|| < 1} C R"(i) x |x 1} C R"(G) x ||xl1} C R"(k) the set of rational numbers, Q C RXr(c)X-(d)1X-10(1I)X: |x1 orC R2(e)CR2(m) Ø (the empty set)X(f)xy 0 R2y2. Let {x&} be a sequence of points in R". For i = 1, .. . , n, let xki denote the ith coordinate of thevector x. Prove that xk a if and only if xkiai for all i = 1, ....n3. Suppose (x} is a sequence of points (vectors) in R" converging to a.(a) Prove that |x all. (Hint: See Exercise 1.2.17.)(b) Prove that if b e R" is any vector, then b xk b a.

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I need help for the proof of question 2. Thank you very much!

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Step 1

Given:

Step 2

To prove:

Step 3

Proof:

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