Q$2(1\mathrm{.}5$ pts$)$ Let A $=\{$Ai$,$j : i in I, j in J$\}$ be a double indexed family of sets. Define sets

X and Y as

X $=[$

i in I

$\backslash$

j in J

Ai$,$j $,$ Y $=\backslash$

j in J

$[$

i in I

Ai$,$j $.$

Show that X $$ Y $,$ but possibly Y $$ X$.$ Hint: It might be helpful to consider a few finite

examples first.