inequality symbols question (beginning algebra) Please help me with this problem:
"In each of the following exercises $x$ and $y$ represent any two whole numbers. As you know, for these numbers exactly one of the statements $x < y, x = y$, or $x > y$ is true.
Which of these is the true statement for each of the following exercises?"

My reasoning is:
e. Since $y$ is not greater than $x$ and $y$ is not equal to $x$ then from this follows that $у$ is less than $x$, which is equivalent to the statement $x > y$ (from the above). So my answer: $x > y$ is the only true statement.
f. Since $y$ is not less than $x$ and $y$ is not equal to $x$ then from this follows that $y$ is greater than $x$, which is equivalent to the statement $x < y$ (from the above).
So my answer: $x < y$ is the only true statement.
Am I right?
(on the image in red color are the answers suggested by the book (i have instructor's copy for self-study) which contradicts with my reasoning...)
P.S. sorry for my English

Yes, your reasoning is right. ::
