Use set identities for the following subproblems: $(15$ pts$)$

$($i$)$ Assuming A and C are disjoint, show that A $\backslash$cap $($B $\backslash$cup C$)=$ A $\backslash$cap B

$($ii$)$ Show that $($A $\backslash$cap $($B $\backslash$C$))\backslash$cap C $=$

$($iii$)$ Show that A $\backslash$ B $=$ A $\backslash ($A $\backslash$cap B$)$