"For the systems below, input $($x$($t$))-$ output $($y$($t$))$ pairs are given. For each system, determine whether it is $($i$)$ memoryless, $($ii$)$ time$-$invariant, $($iii$)$ linear, $($iv$)$ causal, and $($v$)$ stable."

$($a$)y(t)=x(t-2)+x(2-t)$

$($b$)y(t)=[cos(3t)]x(t)$

$($c$)y(t)={\displaystyle \underset{-}{\overset{2t}{}}}x()d$

$($d$)y(t)=\{\begin{array}{cc}0,& t<mn>0</mn>\\ x(t)+x(t-2),& t0.\end{array}$

$($e$)y(t)=\{\begin{array}{cc}0,& x(t)<mn>0</mn>\\ x(t)+x(t-2),& x(t)0.\end{array}$

$($f$)y(t)=x(\frac{t}{3})$

$($g$)y(t)=\frac{dx(t)}{dt}$