Question

在 $xy$ 平面中满足 $x+y\leq5$ 的点中，坐标均为正有理数的点共有：

The number of points with positive rational coordinates selected from the set of points in the $xy$ -plane such that $x+y\leq5,$ is:

$9$

$10$

$14$

$15$

无限多个

infinite

尝试固定其中一个正有理数坐标

Try fixing one positive rational coordinate

一个区间内有无限多个正有理数

There are infinitely many positive rational numbers in an interval

例如，令 $y=1$ 。此时每个满足 $x\leq4$ 的正有理数都给出一个合格点 $(x,1)$ ，而这样的有理数有无限多个。

因此，正确答案是 E。

For example, set $y=1.$ Every positive rational $x\leq4$ then gives an allowed point $(x,1),$ and there are infinitely many such rationals.

Therefore, the correct answer is E.