Consider the set S $=($

$)\backslash$cup $($

$).$ Indicate which statements are true and which statements are false. Justify each decision by analyzing conditions in partition definition.

$\backslash$geoquad $\{($a$,$ b$)$ in

: a $=$b$\}$ and $\{($a$,$ b$)$ in

: $|$a$|$

$|$b$|\}$ form a partition of S$.$

$\backslash$geoquad

$,$

$,$ and

form a partition of S$.$

$\backslash$geoquad

and

form a partition of S$.$

$\backslash$geoquad

and

form a partition of S$.$