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Pretty much just the title. Is it all possible combinations of a and b that have 2 letters ?

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    $\begingroup$ Probably means $\{a,b\}^*\cdot \{a,b\}^*$ where $\cdot$ is the concatenation operation for languages. In this case, its not hard to show that $(\{a,b\}^*)^2=\{a,b\}^*$. $\endgroup$
    – nir shahar
    Nov 2 '21 at 10:44
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    $\begingroup$ It could also mean pairs of words from $\{a,b\}^*$, e.g., $(abba,baaa)$. Depends on the context. $\endgroup$
    – Shaull
    Nov 2 '21 at 11:17
  • $\begingroup$ Don't forget that the empty string, $\epsilon$ is, for example, contained in $\{a,b\}^*$ so $(\{a,b\}^*)^2$ would also include $\epsilon, a$ and $b$. $\endgroup$ Nov 2 '21 at 15:36
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It’s not a standard way to specify a regular or any other language, so any answer would be a guess. Most likely candidates:

A string in (a, b)*, followed by another string in (a, b)*

A string in (a, b)*, followed by the same string again. 

Ask whoever gave this specification for a language.

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