For each of the following statements, state whether it is True or False. If False, please find a contradiction.

a$)$L $(($LR$)$R $=$ L$).$

b$)$L$1,$ L$2(($L$1*$L$2*$L$1*)*=($L$2$ L$1)*).$

c$)$L$1,$ L$2(($L$1$ L$2)*=($L$2$ L$1)*).$

d$)$L $($ L$+=$ L$*).$

e$)$L$1,$ L$2($L$1=$ L$2$ iff L$1*=$ L$2*).$