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What language is generated by the following grammars? In each case justify your answer. 

  1. $S\rightarrow 0S1 \mid 01$
  2. $S\rightarrow +SS \mid -SS \mid a$
  3. $S\rightarrow S(S)S \mid \epsilon$
  4. $S\rightarrow aSbS \mid bSaS \mid \epsilon$
  5. $S\rightarrow a \mid S+S \mid SS \mid S^{\ast} \mid (S)$
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