The statement below is not always true for x, y, an element of all real number.

Question

The statement below is not always true for x, y, an element of all real number. Give an example where it is false, and add a hypothesis on y that makes it a true statement.
"If x and y are nonzero real numbers and x > y, then (-1/x) > (-1/y)."

Explanation / Answer

You are given that x > y, therefore they cannot be the same real number. You need to figure out an example where x > y that makes the statement (-1/x) > (-1/y) false. One potential example is if x is a positive real number and y is a negative real number. In that case, x > y and (-1/x) is not > (-1/y). In order to correct the statement to make it true, you could say that both x and y need to be positive real numbers (this excludes the chance of y being negative and it would still be non-zero.)

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