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Prove or disprove each of the following statements about regular expressions.

1. $(R+S)^{*}=R^{*}+S^{*}$
2. $(RS+R)^{*}R=R(SR+R)^{*}$
3. $(RS+R)^{*}RS=(RR^{*}S)^{*}$
4. $(R+S)^{*}S=(R^{*}S)^{*}$
5. $S(RS+S)^{*}R=RR^{*}S(RR^{*}S)^{*}$

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