$($do not use AI$)$: A causal system of input x$[$n$]$ and output y$[$n$]$ are related through the block$-$diagram

representation shown below. D represents a unit delay and a number on the line represents a

gain.

$($a$)(5)$ Determine the difference equation relating x$[$n$]$ and y$[$n$].$

$($b$)(5)$ Represent the difference equation in $($a$)$ in z$-$domain using z$-$transform.

$($c$)(5)$ Determine the transfer function H$($z$)$ and explain whether the system is stable or not.