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Verify the following identities involving regular expressions.

  1. $R+S=S+R$
  2. $(R+S)+T=R+(S+T)$
  3. $(RS)T=R(ST)$
  4. $R(S+T)=RS+RT$
  5. $(R+S)T=RT+ST$
  6. $(R^{*})^{*}=R^{*}$
  7. $(\in+R)^{*}=R^{*}$
  8. $(R^{*}S^{*})^{*}=(R+S)^{*}$
in Theory of Computation by Veteran (59.1k points)
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