What is the purpose of Tseitin$$s Algorithm? Apply Tseitin$$s Algorithm to turn the propositionalformula $(($p $->$ q$)->($r $->$ s$))->$ t$)$ to CNF$.$

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$))$