is the following true $ (L^R)^* = (L^*)^R $
I tried the following to prove it true. let u,v belong to L then $ L^* = \{ u,v, uu, vv, uv, vu ... \} $ and $ (L^*)^R = \{ u^R, v^R, u^Ru^R, v^Rv^R, v^Ru^R, u^Rv^R ... \} $
now $ L^R = \{ u^R, v^R \} $ so $(L^R)^* = \{ u^R, v^R, u^Ru^R, v^Rv^R, u^Rv^R, v^Ru^R ... \} $