So I know that I want to find $\sum^* - L$ , but I am at a loss regarding how to express that in compact set notation. Any pointers would be appreciated!
2026-03-26 17:51:54.1774547514
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Let $\sum =\{a, b\}$ and $L =\{aa, bb\}.$ Use set notation to describe $L$ complement.
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$$\begin{array}{l}\bar L = {\sum ^*} - L = \{ w|w \in {\{ a,b\} ^*}and\;w \notin \{ aa,bb\} \} \\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \{ \lambda ,a,b,ab,ba\} \cup \{ w|w \in {\{ a,b\} ^*}and\;|w| > 2\} \end{array} % MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaceWGmb % GbaebacqGH9aqpcqGHris5daahaaWcbeqaaiaacQcaaaGccqGHsisl % caWGmbGaeyypa0Jaai4EaiaadEhacaGG8bGaam4DaiabgIGiolaacU % hacaWGHbGaaiilaiaadkgacaGG9bWaaWbaaSqabeaacaGGQaaaaOGa % amyyaiaad6gacaWGKbGaaGjbVlaadEhacqGHjiYZcaGG7bGaamyyai % aadggacaGGSaGaamOyaiaadkgacaGG9bGaaiyFaaqaaiaaysW7caaM % e8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaays % W7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGza % VlaaygW7caaMb8UaaGjbVlaaysW7caaMe8Uaeyypa0Jaai4EaiabeU % 7aSjaacYcacaWGHbGaaiilaiaadkgacaGGSaGaamyyaiaadkgacaGG % SaGaamOyaiaadggacaGG9bGaeyOkIGSaai4EaiaadEhacaGG8bGaam % 4DaiabgIGiolaacUhacaWGHbGaaiilaiaadkgacaGG9bWaaWbaaSqa % beaacaGGQaaaaOGaamyyaiaad6gacaWGKbGaaGjbVlaacYhacaWG3b % GaaiiFaiabg6da+iaaikdacaGG9baaaaa!9D2F! $$
{ x in $\Sigma^*$ : x is not aa and x is not bb }