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1)
| $\in$ | $L$ | $L^+$ | $L^\ast$ | $L^\ast\{c\}^+$ |
|-----------:+:------:+:------:+:----------:+:-----------------:|
| $\epsilon$ | $\bot$ | $\bot$ | $\top$ | $\bot$ |
| $ab$ | $\top$ | $\top$ | $\top$ | $\bot$ |
| $abc$ | $\bot$ | $\bot$ | $\bot$ | $\top$ |
| $bcab$ | $\bot$ | $\top$ | $\top$ | $\bot$ |
| $bcabbc$ | $\bot$ | $\top$ | $\top$ | $\bot$ |
2)
| $\in$ | $R$ | $R^+$ | $R^\ast$ |
|---------:+:------:+:------:+:--------:|
| $(3,3)$ | $\bot$ | $\bot$ | $\top$ |
| $(3,6)$ | $\top$ | $\top$ | $\top$ |
| $(3,18)$ | $\bot$ | $\bot$ | $\bot$ |
| $(3,24)$ | $\bot$ | $\top$ | $\top$ |
5) a) $\{(S, b), (aS, aaS), (b, ab), (ab, aab\}$
b) $\{(S, b), (S, aaab), (aS, aaaaS), (b, aaab), (b, aaaab), (aab, aaaab)\}$
c) $\{ a^n S^x b^{\lnot x} \mid x \in \{0, 1\} \land n \in \N \}$, wobei $\lnot 0 = 1$ und $\lnot 1 = 0$
d) $L(G) = \{ a^nb \mid n \in \N \}$
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