Unformatted text preview: are 2 occurences of ab and 2 occurences of ba.) 3) Let T, W, and X be sets of strings over the alphabet L = {a,b}. Prove or disprove the following statement: if (T ∪ W)* = (T ∪ X)* then W = X. 4) Let T and W be sets of strings over the alphabet L = {a,b}. Prove or disprove the following statement: if T ⊆ W, then (TW)* ⊂ W*. Is it necessarily true that W* ⊂ (TW)*? Prove your answer. 5) Let T, W, and X be sets of strings over the alphabet L = {1,b}. Prove the following statement: ((TW)* ∪ (TX)*) ⊂ (T(W ∪ X))*. Is (T(W ∪ X))* ⊂ ((TW)* ∪ (TX)*)? Why or why not?...
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 Fall '09
 Regular expression, Regular language, Automata theory

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