Real Analysis 1- Using the 2nd photo solution as an example, solve similarly the problem 1B in detail 1. (a) Let E = {q € Q : v2< q < 4}. Find sup E, inf E, max E, and min E if theyexist.(b) Let E = (-1,0) U (0, 1] U {2}. Find the set of interior points of E, the set ofboundary points of E, and the closure of E. 1. (4) The set A=frea:between -T and TT.dam: The interior of A is A° = , Muset of boundary pointy of A is2A- T,町、Prod, daur: let xEA, Than x is a rational nunber between -T and T-TErar] is The set ofvational numbers%3DTheny he density of irrationals, every ogen ball (gen cll) canticaad atx Cantaingirrationals not in A. Hence x is not aninteriór pont of A. Thus he pontA is on interior poit of A. Therefore A° = 4. Sincepout of anyeu set isしgE [T, be arbitrary, herafionuloan interiorpoint, sher' Aisgeu ball (yenuu) Cantered aty Conbainsevey y t [, ] r> ao n A and trrafionals (wof in . Hane, erey yE [m, ] sa beundanyHenvepoiut A. Moreover, no r Ther pomt z # Err, I] is aboudag pout f A becande ureCan finlball centarad atz which dos nor im rerteit A s.DA =[-a,Sine A does nut cmtams all sto boun durs pomta (leke ri) Aynotchocd (horntd.

Answered: Image /qna-images/answer/46ef64e6-4451-4905-b325-783f4341c17a.jpg

Answered: (a) Let E = {q E Q : /2

Linear Algebra: A Modern Introduction

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Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

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