Using the method of Theorem $3\mathrm{.}14$ to prove of disprove each of the following statements about

regular expressions.

$($a$)R(S+T)=RS+RT.$

$($b$)(R+S{)}^{**}=(R^{**}{S}^{**}{)}^{**}$

$($c$)(R+S{)}^{**}=R^{***}+S^{**}.$

$($d$)(RS+R{)}^{***}RS=(R{R}^{***}S{)}^{***}.$