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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?"

enter image description here

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

Daniel W. Farlow
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nonamema
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2 Answers2

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Your reasoning is correct, but your reasoning actually does not contradict the answers suggested in the book.

As voldemort pointed out in a comment, $x>y$ is logically equivalent to $y<x$ [e.g., $3>2$ and $2<3$]. This is due to the symmetric nature of the relations $<$ and $>$. That is, $x>y$ and $y<x$ are logically the same; also, $x<y$ is logically the same as $y>x$. In case you are interested, note that even though the relations $>$ and $<$ have the property of symmetry, they do not possess the property of reflexivity; that is, $x<x$ is not a valid statement.

Daniel W. Farlow
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0

Yes, your reasoning is right. ::

curious_mind
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