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sets A - {x E Q1x < V2} and B-{x E Q|x 2 V2). Our goal in this exercise, is to show that set A has no maximum element and no least upper bound within the set of rational numbers. The following steps will be useful in proving these facts. (a) Assume that q A is the maximum element of A. Show that it must be the case that a2 is the smallest element of set HB (b) Show that it must be the case that q > q. ( e+ . Show that either r E A or r E B. c) Consider the number r - d) Show that either option in the previous step contradicts the assump- tion that q is the maximum element of A (e) Show that the set B has no least element (f) Show that within the set Q, the set A has no least upper boundPlease only typed or clear hand-written guides.

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