Let $L=\{f,g,R,S,c,d\}$ where $f$ is a unary function symbol, $g$ is a binary function symbol, $R$ is a binary relation symbol, $S$ is a ternary relation symbol, and $c$ and $d$ are constants. State whether each of the following are formulas of $L.$ For those that are, prove it $-$ i$.$e$.,$ show how they are built up from the atomic formulas. $($When citing the definition of a formula, please be consistent with the way the clauses are numbered in the notes.$)$

$($a$)R(c,x_1)=d$

$($b$))=(c$

$($c$))=(f(x_2)R(d,d)$

$($d$)S(c,f(x_1))$