Q$5)$ Construct PDAs that accept the following languages:

$($a$)L_b=\{wc{w}^R$:win$(a+b{)}^{**}\}.$

$($b$)L_c=\{a^n{b}^{n+m}{c}^m$:$n0,m1\}.$

$($c$)L_d=\{w$:$n_a(w)+n_b(w)=n_c(w)$:win$(a+b+c{)}^{**}\}.$

$($d$)L_d=\{a^n{b}^{n+3}$:win$(a+b{)}^{**},n0\}.$