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)  $L(G) = \{ a^nb \mid n \in \N \}$