\item Assume you have an alphabet consisting of the letters

      $a$, $b$ and $c$ only. (1) Find a regular expression

      that recognises the two strings $ab$ and $ac$. (2) Find

      a regular expression that matches all strings

      \emph{except} these two strings. Note, you can only use

      regular expressions of the form 

      \begin{center} $r ::=

      \varnothing \;|\; \epsilon \;|\; c \;|\; r_1 + r_2 \;|\;

      r_1 \cdot r_2 \;|\; r^*$ 

      \end{center}

\item Define the function \textit{zeroable} which takes a

      regular expression as argument and returns a boolean.

      The function should satisfy the following property:

$\textit{zeroable(r)} \;\text{if and only if}\; L(r) = \varnothing$

      consisting of numbers, left-parenthesis $($,

      right-parenthesis $)$, identifiers and the operations $+$,

      $-$ and $*$. Can the following strings in this language

      be lexed?

  \item $(a + 3) * b$

  \item $)()++ -33$

  \item $(a / 3) * 3$

In case they can, can you give the corresponding token

sequences.