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  3. 3 define the sets a b c q by and...

Question: 3 define the sets a b c q by and...

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3. Define the sets A, B C Q+ by and let f(x) 22. (a) Sketch the graph of f in the coordinate plane. (b) Let a E A be arbitrary. Use the points (a, a2 -2) and (2,2) on the graph of f to find a rational y such that y > a and <2. Deduce that A has no largest element. (c) Let be B be arbitrary. Use the point (b,b2-2) on the graph of f to find a rational y such that y < b and y2 > 2 Deduce that B has no smallest element. (d) Prove that A is nonempty and bounded above. (e) Prove that b Q is an upper bound for A if and only if be B. (f) Prove that sup A does not exist in Q, and deduce that Q does not have the least upper bound property.

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