FSM的問題

(i)What is the set generated by the following phrase-structure grammar? G=(V,T,S,P), V={0,1,S}, T={0,1}, P={S->01,S->0S1}

這題答案是:

{0^n1^n n>=1}

(ii)Construct a phrase-structure grammar to generate the set {1^n0 n>=0}

這題答案是:

G=(V,T,S,P), V={0,1,S}, T={0,1}, P={S->1,S->0,S->S0}

是這樣嗎?
如果有錯 請助教能多多教我一下