### A Man’s A Man Who Looks A Man Right Between The Eyes

3. Let $U= \{0, 1, 2, 3, 4, 5, 6\}$ be the Universal Set (for this problem) and let $X=\{0,1,2,3\}$, $Y=\{0, 3, 6\}$, and $Z=\{0, 5\}$.

Compute the given sets. (Remark: we will have shown that set difference is not associative).

$(X-Y)-Z$
$X-(Y-Z)$
$Y^c \cup Z^c$
$X \cap X^c$

Again (sorry for the child’s play). A poor workman blames his tools; this doesn’t make him wrong. Obviously X – Y is (the set) {1, 2}. It follows then that (X-Y) – Z is also {1, 2}.

Whereas, in light of the fact that Y – Z = {3, 6}, one has X – (Y-Z) = {0, 1, 2}.

Anybody (outside a math class) pretending to want an explanation of what (if anything) has gone wrong is, pretty reliably, actually looking for some weakness whereby they can undermine somebody’s authority.

The classic blunder at this point is to refuse to take such a student seriously. And yet, they’re doing what I would’ve done; what I’ll go out on a limb and guess you would have done. Students didn’t just become stupid because you got an advanced degree any more than kids got to be some inferior order-of-being just because you decided to call yourself a growup.

How are they to know that, here in math class, we mean what we say? When, in every other arena (and for all we know, this one), authority rules?

(Yes, yes… they call it “opinion” and blame it on “the people”. Are we bored yet?)