$3.$ Let L $=\{$g$,$ S$,$ d$\},$ where g is a binary function symbol, S is a ternary relation symbol, and d is a constant symbol. Prove or disprove each of the following, using only $($and any$)$ material covered to the end of the Week $9$ Slides. $($a$)\{$gdd$$d$,$xx$$d$\}|=$x$$ygxy$$d$($b$)($Sxyz $($w$$z gwz $$ x $$ Sxyz$))$ is logically valid.$($c$)$ gx$1$x$2$d$$gx$3$x$4$d$($d$)\{$gxy $$ d$,$ Sddd$,$x$$y gxy $$ d$\}$ is satisfiable.