State with justification if each of the following sentences of predicate logic is logically valid.

$($i$).($x$$y$$zS$($x$,$ y$,$ z$))->($x$$y$$zS$($x$,$ y$,$ z$))$

$($ii$).($x$$y$$zS$($x$,$ y$,$ z$))->($u$$v$$wS$($u$,$ v$,$ w$))$

$($iii$).($x$$y$$zS$($x$,$ y$,$ z$)->($x$$y$$zS$($x$,$ y$,$ z$))$

$($iv$).($x$$z$$yS$($x$,$ y$,$ z$))->($x$$y$$zS$($x$,$ y$,$ z$))$