Which of the following would be a valid partition of the set of all strings A^* over the alphabet $A = \{a, b\}$ A = \{a, b\}?

Question

Which of the following would be a valid partition of the set of all strings   A^*  over the alphabet   A = \{a, b\} ?

Answer

\{ A^n : n\in\mathbb{N} \}

Answer

\{\{\epsilon\},\{	ext{all strings starting with a}\}, \{	ext{all strings starting with b}\}\}

Answer

\{\{	ext{aa}\},\{	ext{ab}\}, \{	ext{ba}\}, \{	ext{bb}\}\}

Answer

There is no way of partitioning the set, because it's an infinite set.

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