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Question: 32 points problem 8 proof methods a use a direct...

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32 points Problem 8: Proof Methods (a) Use a direct proof to prove, that for all real numbers a and b if ab 3 then a2 6b9. (b) Use a proof by contraposition to prove, that for all real umbers a and b if a+b22 then a 1+V2 or b2 1-V2.

(c) Use a proof by contradiction to prove, that for all real numbers a and b if ab s 1/2 then a2 tab >-2 or b2 > 1. (d) Provide a counterexample to disprove, that for all real numbers r if then 221/2 No explanation is needed for how the counterezample was found. Make sure to provide a verification that the counterezample is correct.)

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