It is claimed that the following inequality is true for all negative numbers x and y: The

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It is claimed that the following inequality is true for all negative numbers x and y:


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The following proof is offered by a student:


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a. Explain the error made by the student.


b. By use of a counter-example, verify that the inequality is not satisfied if both x and y are negative.


c. Prove that this inequality is true if x and y are both positive.

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