### Examine Other Beauties

5. Let $Y = \{0,3,6\}$ and $Z = \{0,5\}$ again;
compute a. $Y\times Z$ and b. $Z \times Y$.

Obviously $Y\times Z =$
{
(0,0), (0,5),
(3,0), (3, 5),
(6,0), (6, 5)
}

and

$Z\times Y$=
{
(0,0), (0,3), (0,6),
(5,0), (5,3), (5,6)
};

what’s more, almost all my students
knew it on the day (typically in the form
$Y\times Z =\{ (0,0), (0,5), (3,0), (3, 5), (6,0), (6, 5)\}$
and
$Z\times Y =\{(0,0),(0,3),(0,6),(5,0),(5,3),(5,6)\}$
). it bothers me
not at all that they don’t seem much
to care about my typographical
conventions; the main thing is that
they know… and are willing to *admit*
that they know (in writing) how a
“cross-product” (what our text,
alas, insists on calling a “cartesian”
product) can be written out in
“set-of-ordered-pairs” notation.

6. Let $U = \{0, 1, 2, 3, 4, 5, 6\}$ again.
Write out the Relation $R$ defined on $U$ by $xRy \equiv 3 | (x - y)$.

Don’t forget that “a-b” is meaningful even when $b \ge a$; otherwise there are no systematic errors classwide. OK. I’m a liar.
There’s this. Remember that the answer is (i) a set (in our context, written as a list of items, between set brackets, and separated by commas), of ordered pairs (each of which, in our context, is written between ordinary parentheses… what’s weird about all this is that it’s perfectly easy to get students to care about keystroke-perfect code when a robot grades their work but they’ll mortgage their god-damn grandmothers to get you to give ’em some special deal as soon as some hint of “humanity” comes into the picture.).